The world number two broke in the last game of the first set to claim the opener, before the Swiss drew level with a tiebreak win in the second.
However, the Serb clinched two breaks in the decider to allow himself to coast to a win.
Read how all the action unfolded below:
7.47pmGood evening. Novak Djokovic and Roger Federer should be heading out for their ATP World Tour Final round robin match in around 15 minutes. On paper, this should be one of the most exciting of the round robin contests this year.
7.50pmThis is a tournament that both players are used to winning. Djokovic won his second title in 2012, while Federer has taken victory in this competition six times between 2003 and 2011. Since the Finals moved from Shanghai to London, these two players have won three of the four tournaments.
7.53pmWhichever player loses this match will face a battle to reach the semi-finals, as they share a group with former US Open champions Juan Martin del Potro and world number nine Richard Gasquet. In their meeting yesterday, it was the Argentinian that took victory.
7.56pmAs I mentioned in the introduction, Federer has the edge over the world number two in their head-to-head record, beating his 16 times in their 30 previous matches. However, the Swiss has not beaten Djokovic this year, and has won just three of their last 11 meetings.
7.58pmAs the players' details are being read to the crowd, there's a moderate cheer for Djokovic, but it sounds like the majority of the fans are behind Federer this evening.
8.01pmThe players have both left their dressing rooms and are getting ready to head out onto the court in the O2 arena. Naturally, it's a sell-out crowd at the venue for this evening's match.
8.04pmFederer is the first of the two players to make his way out. As expected, it's a huge cheer for the former world number one, who has won this tournament six times. Djokovic follows, but it definitely sounds like it's Federer who has the bulk of the support tonight.
8.07pmDjokovic wins the toss, and the players are just starting their warmups ahead of tonight's match. We shouldn't be too far away from the start of this clash now.
8.09pmAhead of today's match, Djokovic has called for this tournament to be played in different locations. The 26-year-old told reporters: "The tournament should definitely be organised at different places and not held in one city for more than three years. Various players share this opinion and believe it should be played in places where our sport, which is a global one, is not so popular which means it could expand."
8.12pmThe players finish their warmups, grab a quick drink and are ready to go. Djokovic is serving first.
Djokovic 1-0* FedererFederer looks to come into the net early on, but he mis-hits his shot into the net, before smashing a return long on the next point. Djokovic drops his first point by challenging a call on the sideline, but hawkeye showed that Federer's cross-court backhand was clearly in. However, Djokovic is able to wrap the game up as Federer misses another couple of returns.
Djokovic *1-1 FedererAfter clinching the opening point, Federer gets dragged into a lengthy rally and tries to force a winner, but puts too much power on the ball. Djokovic keeps himself in the gain again with a superb double-handed backhand down the sideline, but Federer responds with the first ace of the match, before a long return from Djokovic on the next point allows him to hold.
Djokovic 2-1* FedererDjokovic reaches slow to make another good backhand, but Federer responds well with a forehand down the sideline. The Serb makes a couple of shots from the net, forcing a mistake from the six-time champion. At 40-15 up, Djokovic just has to make a shot into an open court, but he slices his backhand well wide. However, Federer finds the net on the next point to keep the opening set on serve.
Djokovic *2-2 FedererIt's a relatively straight-forward service game for Federer. His first two serves are not returned, before a long forehand from Federer gives Djokovic his sole point of the game, before the Swiss player quickly wraps it up with another couple of strong serves.
Djokovic 3-2* FedererDjokovic holds again, but does not look entirely comfortable yet this evening. Despite this, Federer struggles to return the Australian Open champions' serve, allowing him to swiftly wrap up another game.
Djokovic *3-3 FedererFederer looks really focused in this first set, racing to 40-0 before sending another ace past the world number two. The Swiss player has got 73% of his first serves in so far tonight.
Djokovic 4-3* FedererFederer tries to attack from the back of the court but forces his forehand just long. He makes the same mistake on his backhand on the next shot, giving the Serb a 40-0 lead, but a mistake from the defending champion at the net keeps Federer is the game, but he misses the baseline with his forehand again on the next point. Neither player has faced a break point so far this evening.
Djokovic *4-4 FedererFederer starts well but makes a double fault to give Djokovic some hope. The Serb edges ahead in the game after a scuffed effort from Federer, but the Swiss draws level after a looping forehand effort from the world number two goes just wide. Djokovic's forehand goes long again on the next shot, and he smashing the ball into the net in frustration, before returning Federer's serve to the net on the next shot to allow him to hold serve. That could have been a tricky situation for the Swiss, having found himself a point down, but he recovered well.
Djokovic 5-4* FedererDjokovic makes his first double fault of the match, before losing his footing to give Federer a 30-15 lead. The Serb recovers well, jumping to reach a Federer return, lobbing the ball past his oppoenent. However, another double fault brings up the first break point of the match. Federer looks to have the reigning champion beaten, sending a backhand to the sideline, but it was called wide by the sideline judge, taking the game to deuce. Djokovic gets advantage when the world number seven hits the ball long, before escaping from the game with his serve intact when his opponent mis-hits a forehand return. Djokovic had looked strong on serve early on, but his first serve percentage has dropped to 51% following that game.
8.50pmFacing a break points seems to have focused Djokovic, as he comes out attacking and claims the opening point, but a superb volley soon draws Federer level. Federer twice clips the net chord, but Djokovic manages the read it well to edge back in front, before a stunning return from the Serb sees Federer slice the ball well long, bringing up two set points. The world number seven escapes the first with an overhead lob at the net, but he fires long on the next point to give Djokovic a one-set lead.
8.52pmIt's a cruel end to the first set for Federer. The six time ATP World Tour Finals winner looked the stronger player in the early stages of the set, but missing an opportunity to take a break in the ninth game gave Djokovic the chance he needed.
Djokovic 6-4 1-0* FedererDjokovic's strong finish to the first set appears to have carried over into the start of the second. The Serb open with some strong serves to take a 30-0 lead before Federer catches him out with a brilliant forehand. The Swiss then gets into a lengthy rally with his opponent before finding the net. Another good serve from the world number two allows Djokovic to clinch the opening game of the second set.
Djokovic 6-4 *1-1 FedererDjokovic seems to have taken his game up a level, as he glides around the court to take the opening points, before appearing the have his opponent beaten again, only to fire the ball long. A long forehand from the world number seven leaves him facing two break points, however Djokovic twice sends the ball long to allow Federer to fight back to deuce. After forcing advantage for a second time, Federer finds a big serve, which Djokovic can't return. That's a huge hold of serve for the Swiss player.
Djokovic 6-4 2-1* FedererAt 15-15, Djokovic serves his first ace of the match, before winning the next point with a sliced volley while moving into the net. Federer blasts his return well long to give Djokovic the game. While the Serb may be disappointed not to be a break up in this second set, he's looking ever more comfortable during his own service games.
Djokovic 6-4 *2-2 FedererFederer makes sure that he doesn't face another fight on his serve, putting in some powerful first serves, before throwing in some serve-and-volley to keep Djokovic guessing, before coming in from the baseline to fire his forehand past the Serb and wrap up the game to love.
Djokovic 6-4 2-3* FedererBREAK! Djokovic quickly takes a 40-0 lead, but Federer fights back, winning a points against Djokovic's second serve for the first time in this set, while a slice into the net from the Serb followed by a mis-timed backhand brings the game to deuce. A stunning backhand effort from Federer just finds the sideline, giving him a break point, which he takes when Djokovic sends his forehand well long.
Djokovic 6-4 *3-3 FedererBREAK BACK! At 15-15, Federer tries a drop shot, but Djokovic manages to scramble in from the back of the court to make the return. The Swiss levels with an ace, before a shot into the net from each player sends the game to deuce. A mistake from the world number two gives Federer advantage, but another double fault returns the game to deuce. The defending champion gets a lucky contact with the net chord to give himself a break point, and he's able to seal the game when Federer makes his second double fault of the game.
Djokovic 6-4 3-4* FedererBREAK! Djokovic looks suddenly weary, and makes a string of errors, including a wildly long backhand, to give Federer three more break points. The Serb tries to keep himself in the game by coming into the net, but Federer spots the danger, and makes a stunning slices backhand to the sideline to go a break ahead again. Both players know that this is a crucial stage of the match, and neither seem to be able to take control.
Djokovic 6-4 *3-5 FedererDjokovic seems to have no energy in his legs at the moment, but he's still able to make some strong shots to take a 30-15 lead, before a big serve from Federer brings the scores level. A fierce cross-court forehand from Djokovic goes well wide, giving Federer the change to consolidate his break, but he drags his backhand down the sideline just wide, much to the frustration of the crowd, he are still mainly cheering for the Swiss player. However, a couple more errors from the world number two allow Federer to hold onto his serve, despite having just 45% of his first serves in in this second set.
Djokovic 6-4 4-5* FedererA spectacular rally, which saw both players come into the net, results in a point for Djokovic, giving the world number two a 40-15 lead as he serves to stay in the set. A return to the net from Federer means that the world number seven will have to serve for the set.
Djokovic 6-4 *5-5 FedererBREAK BACK! Federer starts well as he looks to level the match, but a long ball from the world number seven allows Djokovic to level the game. A superb serve from the Swiss brings up set point though, but he sends a forehand long to give the Serbian another chance, and he manages to force break points with a stunning cross-court forehand, despite a brilliant backhand from Federer almost wrong-footing him. Federer initially manages to escape, but the world number two gets another chance, getting the break back when Federer tips his backhand into the net.
Djokovic 6-4 6-5* FedererDjokovic looks to be back on form on serve as he races to a 40-15 lead, but Federer fights back, forcing a series of errors from the defending champion to bring up deuce. Federer has the first chance to seal the game, but Djokovic regains his rhythm from early in the game to lead the set for the first time in eight games. Djokovic will get at least a tiebreak from this set.
Djokovic 6-4 6-6 FedererThe players are warned that the review system, Hawkeye, has gone offline, so they can't make challenges at the moment, but Federer takes control of the game with an ace, but is unable to get the better of Djokovic in an exchange at the net. However, Federer is able to wrap up the game, so we'll have a tiebreak.
10.01pmFederer plays superbly throughout the tiebreak to take this match to a deciding set. The Swiss is moving superbly around the court at the moment, while Djokovic is looking a little drained.
Djokovic 6-4 6-7 *1-0 FedererBREAK! After performing so well to win the second set, Federer seems to have gone off the boil at the start of the decider, as makes a series of errors to give Djokovic three break points, and he converts when Federer fires his forehand long. It's the perfect start to this set for the defending champion.
Djokovic 6-4 6-7 2-0* FedererDjokovic is struggling with his backhand, smashing the ball into the net to give Federer the lead in the game, but a poor return from the Swiss on the next point levels the scores. However, Djokovic sends the ball long again to give his opponents a chance to break back straight away, but he puts too much power behind his forehand, taking the game to deuce. Djokovic forces advantage several times as he tries to clinch the game, eventually managing to get the better of the Swiss with a potent cross-court forearm just short of the two-hour mark in this mark.
Djokovic 6-4 6-7 *2-1 FedererIt's a superbly confident service game from Federer, which he needed to give himself a chance in this final set. He quickly clinches a 40-0 lead before sealing the game with an ace.
Djokovic 6-4 6-7 3-1* FedererDjokovic looks to be in control again as he races to a 40-15 advantage, but he tries too hard in his bid the seal the game, slicing his drop shot short, but an ace allows him to clinch the game on the next point.
Djokovic 6-4 6-7 *4-1 FedererBREAK! Djokovic edges ahead after making a superb backhand, despite appearing a little sluggish after the previous game. He brings up two break points after forcing an error from Federer, but mis-hits his forehand, smashing the ball high into the O2 arena to allow Federer to remain in the game. The world number seven fights hard in a lengthy rally, but Djokovic shows plenty of pace behind the baseline to match his opponent, before Federer slices his shot wide, leaving the Serb well in control of the deciding set.
Djokovic 6-4 6-7 5-1* FedererFederer looks a broken man as Djokovic quickly wraps up another game, leaving him just one short of victory in his opening game of the tournament. The Serb wraps up the game with two superb aces, just clipping the sideline on both occasions.
Djokovic 6-4 6-7 *5-2 FedererFederer plays some of his best shots to force Djokovic to have to serve out the match. He comes into the net for a volley, before sending a big serve past Djokovic to take a 40-15 lead. However, the world number two makes some impressive returns to take the game to deuce, but Federer rallies to keep himself in the match.
10.34pmDjokovic sends an ace past Federer to give himself three match points.
10.35pmGAME, SET & MATCH! Novak Djokovic 6-4 6-7 6-2 Roger Federer
10.36pmIn the end it's a clinical finish from the world number two to secure a win in his opening match at the ATP World Tour Finals. For Federer, it will be an uphill struggle to reach the semis from here, with matches against good opponents still to come in the round robin.
10.37pmThe result does in fact leave Djokovic top of group B, while Federer sits bottom. The Serb showed signs of fatigue from his win in the Paris Masters at the weekend, but in the end he just had enough to peak at the tight moment and clinch victory.
10.39pmWell that's all from the O2 Arena this evening, but join us again tomorrow for the third day of the tournament, when world number one Rafael Nadal will be in action against Stanislas Wawrinka, while David Ferrer will play Tomas Berdych. Until then, thanks for joining me this evening, goodbye.