The third seed needed just over two hours to beat the world number 105 6-1 6-4 7-5.
The defending champion will play Blaz Rola of Slovenia in his next match later this week.
Read how all the action unfolded below:
1.01pmGood afternoon! The players are ready to head out onto the famous Centre Court at Wimbledon as Andy Murray prepares to start the defence of his title. David Goffin leads them out, with Murray receiving a standing ovation from the crowd, which includes his mother Judy Murray and British tennis player Ross Hutchins.
1.03pmThe umpire meets with the players for the pre-match coin toss. It looked like Goffin won it, although the court microphone didn't pick up whether he chose to serve or receive first.
1.05pmThis will be the first meeting between these two players. Goffin made a bit of a name for himself with a run at the French Open a couple of years ago, before eventually being knocked out by Roger Federer. The Belgian has been struggling for form this year, with the majority of his wins coming on the challengers tour, but he managed a couple of wins on grass at Eastbourne last week.
1.07pmGoffin has only played at Wimbledon twice before, reaching the third round on his debut at the tournament in 2012, but exiting in the first round last year.
1.09pmMurray's record at SW19 is somewhat more illustrious. After making his debut as a teenager in 2005, the Scot has missed one tournament through injury, but has progressed further every year until he lifted the trophy last summer. He's never been knocked out before the third round!
1.10pmSo the warm-ups are over and the umpire confirms that Goffin chose to receive, so it's Murray to serve first.
Murray 1-0* GoffinIt's a pretty straight-forward start to the match for Murray. The Brit races to a 40-0 lead as Goffin fires a couple of shots long. The Belgian makes a solid return to keep himself in the game before Murray tries an ambitious sliced backhand which drifts wide, before wrapping the game up with an ace.
Murray *2-0 GoffinBREAK! There are some obvious nerves from the Belgian as he misses two of his opening three first serves, allowing Murray to come in from the baseline an attack, forcing a couple of errors from the world number 105. Goffin mistimes a cross-court forehand as he sends the ball into the net to give Murray a chance to break, but his forehand goes just wide as he tries to wrap up the game. However, Goffin's nerves continue as he fires long on back-to-back points to give Murray the break.
Murray 3-0* GoffinAt 15-15, Murray trips but he recovers quickly and manages to win the point. At first it looked like he was reaching for his ankle, but he appeared more concerned with the state of his trainers! As the game got back underway, Goffin produces a brilliant lob before coming into the net for a volley, but a fractionally long forehand from the Belgian allows Murray to hold the game.
Murray *3-1 GoffinGoffin starts the game well, coming into the net to smash a winner post his opponent, but a couple of balls to the net allow Murray to take the lead. However, the Belgian dips deep to win the next two points before pressuring Murray with a volley, which the Scot can only return wide to give Goffin his first game of the match.
Murray 4-1* GoffinMurray admitted that he would be nervous starting the defence of his title, and that shows a little during this game as he makes the first double fault of the match, before needing his second serve on the next point. However, Murray deceives Goffin with a good forehand, resulting in the Belgian losing hit footing at the same end the Murray slipped earlier on. Initially he appears to be in a little pain from his fall but he quickly shakes it off, but can't prevent Murray from wrapping up the game.
Murray *5-1 GoffinBREAK! Goffin produces some solid groundstrokes from the back of the court to claim the opening point of the game, but Murray is soon back in control as the Belgian makes his first double fault. Murray looks to capitalise on his opponent's inconsistency as he ups the tempo and comes into the court for a powerful forward to give himself two break points before sealing the game with a looping shot to the baseline. It's impressive stuff from the world number four.
1.39pmSET! Andy Murray 6-1 David Goffin
1.40pmSo after a little under half an hour, Murray has wrapped up the opening set. It wasn't an easy game to seal the set, with Goffin continuing to look lively from the back of the court, but Murray had just too much on the crucial points.
1.41pmGoffin has shown promise in the opening set, with some brilliant shots from the baseline and a couple of useful approaches to the net. If he can keep his serve tidy, he should be able to make the second set a lot tighter.
Murray 6-1 *0-1 GoffinMurray takes the first two points, clinching the second with a stunning forward to the sideline, but Goffin fights back, showing superb pace around the court before sending a forehand down the line. Goffin makes a double fault to send the game to deuce, but quickly picks up advantage with his first ace of the day before another strong first serve is too much for Murray to return.
Murray 6-1 1-1* GoffinIt's a comfortable hold for Murray as he appears to have upped the intensity on his serve at the start of this second set, forcing return errors from Goffin to allow him to quickly take the game.
Murray 6-1 *2-1 GoffinBREAK! Goffin starts the game with a clumsy error, tapping the ball into the net before slicing wide later in the game to give Murray the chance to get the break. Goffin stretches his opponent with some well-placed shots to the baseline before sending a forehand drive past the British number one to save the first break point, but smashes his forehand well wide on the next point to give Murray the lead.
Murray 6-1 3-1* GoffinGoffin takes a rare lead in a Murray service game when the Brit sends his forehand just wide before the Belgian beats him with a solid return. However, Murray ups his game, firing the fastest serve of the match so far at 121mph past the world number 105.
Murray 6-1 *3-2 GoffinGoffin manages to find some consistency to take a 40-0 lead, but a good Murray keeps the game alive after forcing a mistake from the Belgian during a rally, but he can't overturn Goffin's lead as the third seed slices his backhand into the net.
Murray 6-1 4-2* GoffinMurray really is rattling through his service games now as he fires a 131mph ace past his opponent on his way to a hold to love. Goffin has certainly been better in this second set, but hasn't really been able to test the Murray serve at all today.
Murray 6-1 *4-3 GoffinAt 30-30, Murray comes into the net for a drop shot, which Goffin stretches to return, but can't return to the other side of the court to reach Murray's volley, which gives the defending champion a chance for another break. Goffin forces the game to deuce, before digging deep to see out the game with an overhead smash. He's still a break down in this set, but isn't out of it yet.
Murray 6-1 5-3* GoffinA poor forehand down the line fails to clear the net for Goffin as Murray quickly takes the lead in the game. He tries the same shot against later on but it yields the same result before Murray gets the better of him on the next point with a cross-court backhand to clinch the game while Goffin takes a tumble again trying to return it, but once again he seems to be alright.
Murray 6-1 *5-4 GoffinMurray attempts to attack the Goffin serve as he looks to wrap the set up, but the Belgian serves well to make it difficult for the Brit. At 40-15 up, Goffin comes into the net facing an easy overhead smash into an open court to wrap up the game, but he misses it, though manages to wrap the game up when Murray misses a return on the next point. However, the third seed will be serving for the second set next.
2.19pmMeanwhile, here's a shot of some of the famous famous in the royal box on Centre Court today:
2.21pmSET! Andy Murray 6-1 6-4 David Goffin
2.23pmMurray wraps up the second set, comfortably racing to a 40-0 lead before Goffin slipped while coming into the net firing his shot long. He certainly played better in the second than in the opener, but it really has looked like a formality for Murray so far.
Murray 6-1 6-4 *0-1 GoffinGoffin starts confidently with an ace before Murray hits back with a couple of powerful shots from the back of the court. Murray has a chance for an early break when Goffin directs a forehand just wide, but the game heads to deuce following a good serve from the Belgian. Goffin gets advantage before Murray challenges a call on the baseline, but he gets in wrong as Goffin's shot was comfortably in, giving him the game.
Murray 6-1 6-4 1-1* GoffinWell Murray certainly isn't hanging around on his own service games as he wraps up another to love. With Goffin still yet to really challenge his opponent's serve, Murray must be keen to get another look at the Belgian's serve as he tries to wrap up this match.
Murray 6-1 6-4 *1-2 GoffinThe pair share the opening four points of the game before Murray breaks a string on his racquet while returning the Belgian's serve. While he adjusts to his new strings, Goffin is able to wrap up the game to keep the third set on serve for now.
Murray 6-1 6-4 2-2* GoffinGoffin gets a bit of luck at the start of the game as he gets a lucky hit on the net chord the claim the opening point of the game. The Belgian uses the momentum to take the next point as he moves swiftly around the court, before a punchy forehand to the back of the court gives Goffin his first break points of the match. Having looked a little flat at the start of the game, Murray manages to find his form to take the game to deuce, before two long returns allow Murray to escape with his serve intact. That will be a big blow for his opponent.
Murray 6-1 6-4 *2-3 GoffinYou'd have forgiven Goffin for letting his head drop a little after losing the last game, but he serves well to quickly take a 40-0 lead, aided my Murray slipping in the opening point of the game. However, the mistakes return as Goffin makes a double fault before hitting his forehand long. Goffin produces a fantastic shot to wrap the game up though, hitting his backhand on the move to just pick out the sideline and keep him in this third set.
Murray 6-1 6-4 3-3* GoffinIt looks like being a much simpler service game for Murray this time around as he quickly opens up a 40-0 lead. Goffin tries to extend the game and picks up a point with a strong forehand, but can't prevent Murray securing the game on the next point.
Murray 6-1 6-4 *3-4 GoffinGoffin is really starting to look quite settled during his own service games. Murray returns well to prevent the Belgian from coming into the net, but Goffin plays well from the back of the court to seal the game.
Murray 6-1 6-4 4-4* GoffinSome confident serving from Murray helps him race to another hold to love, keeping the scores level in this third set. It feels like we could be heading towards a tiebreak in this set.
Murray 6-1 6-4 *4-5 GoffinMurray makes some big returns to take the came to deuce as he continues to look for his first break of the set. However, it's Goffin who claims advantage with a good shot the the baseline. Murray takes it back to deuce when he picks out the sideline with a forehand shot of his own on the next point, but back-to-back efforts into the net allow Goffin to keep his serve in tact.
3.03pmWEATHER WATCH! It was pretty bright out on Centre Court when this match got underway, but there are some noticeably dark clouds forming overhead. If Goffin does manage to force this into a fourth set, the roof may have to be called into action.
Murray 6-1 6-4 5-5* GoffinWell if there is to be some rain, Murray is certainly trying to make sure he doesn't get caught in it as he quickly notches up another hold of serve without Goffin getting a single point on the board.
Murray 6-1 6-4 *6-5 GoffinBREAK! Initially, Goffin continues to serve well as he has done throughout much of the third set to open up a 40-0 lead. Murray comes in fro the back of the court to get a point back at the net before Goffin hits the ball long on the next point. The Belgian picks a poor time for another double fault, allowing Murray to claw the game back to deuce. Murray's resurgence seems to unsettle Goffin as he hits the ball long two points in a row to give Murray the game, and the defending champion now has the chance to serve for the match.
3.12pmMurray comes back from 0-30 down to bring up match point.
3.13pmGAME, SET & MATCH! Andy Murray 6-1 6-4 7-5 David Goffin
3.14pmIt's the perfect ending to the match for Murray as he fires an ace down the line to wrap up proceedings. Goffin put up a good fight at the start of the game as he tried to force the set to a tiebreak, but ultimately Murray was just too strong for the world number 105. He receives a big cheer from the crowd as he makes his way off, as does Murray when he follows a few moments later.
3.16pmNext up for Andy Murray will be Slovenia's Blaz Rola, who came through against Pablo Andujar in straight sets a short time ago. That match will take place later this week.
3.17pmWell that's all from Centre Court for now, but join us again later this afternoon when top seed Novak Djokovic begins his campaign against Andrey Gokubev. Until then, thanks for joining me this afternoon, goodbye!