Bournemouth pressed for an equaliser but in the first minute of added-on time, Sanchez scored his second to earn Arsenal a first win in four games.
Read below to see how the action unfolded at the Emirates Stadium.
1.16pmHello, and welcome to Sports Mole's live coverage of the match in the Premier League between Arsenal and Bournemouth.
1.19pmAfter Chelsea, Manchester City and Liverpool all came through closely-fought matches on Saturday, Arsenal suddenly find themselves six points off the pace in the Premier League table but they can close the deficit on the trio in front of them with victory this afternoon. However, they face a Bournemouth side who were boosted by a win over Stoke City last weekend and Eddie Howe's men can establish themselves inside the top half of the standings with a surprise triumph this afternoon.
1.22pmBefore we get onto the team news, let me bring you an update on the game which is currently taking place at Vicarage Road between Watford and Stoke City. The result could have ramifications on where Bournemouth end the afternoon in the table and as it stands, it's Stoke who lead thanks to a goal from Charlie Adam. There's just under 30 minutes left in that one.
1.23pmRight then, let me bring you some team news. There's a forgotten face in one of the starting lineups...
1.30pmIt's often that Arsene Wenger makes so many changes but he has done this afternoon. It's seven, to be precise, with the big news being the return of Mathieu Debuchy - his last appearance for Arsenal was on November 24, 2015!
Theo Walcott and Alex Oxlade-Chamberlain are also back in the team while Granit Xhaka is given a start in midfield alongside Mohamed Elneny. Aaron Ramsey and Olivier Giroud are the major names to miss out.
1.34pmAs for Bournemouth, Eddie Howe has made two alterations to the team which won at the Britannia Stadium last weekend. Jack Wilshere has to sit this one out with the game coming against his parent club. The players coming into the team are Brad Smith and Adam Smith. Nathan Ake keeps his place having scored the winning goal against the Potters but Benik Afobe starts on the bench on his return to Arsenal.
1.39pmHEAD TO HEAD! Given Bournemouth's rise up the divisions, these two teams have barely met in competitive fixtures with just three matches having taken place in the past. They have all ended in an Arsenal victory and a clean sheet for the Gunners so I suppose it can only get better for the Cherries!
1.42pmLast season's contest at the Emirates Stadium ended in a 2-0 victory over the Gunners. Click here to have a look back at the game!
1.45pmWe can't go through this build-up without talking about Jack Wilshere. The midfielder isn't playing this afternoon due to the terms of his loan agreement but that's not to say he hasn't been a talking point this week. There have been plenty of rumours regarding his future but Arsene Wenger had this to say when talking about the subject earlier this week.
1.50pmWhen we look back at Wilshere's early months at Bournemouth, it has to be considered a success. There are always doubts over his fitness but so far, he has featured in nine Premier League matches this season after missing all but a few minutes of the last campaign. He seems a class above Bournemouth but he may have not got so many opportunities at other teams so it definitely appears to be the correct move for the 24-year-old. He will be disappointed to miss out this afternoon but a return to the Emirates may make it clearer for him to make decisions over his future.
1.55pmWhile he has been touted as a future manager of Arsenal, Bournemouth boss Eddie Howe won't be using this afternoon as an audition to impress the Gunners owners. He is continuing to work wonders down on the South Coast and it's still remarkable that a club of their size is going into a Premier League fixture at the end of November with an opportunity to establish themselves in the top of the table. Reaching 40 points will still be his primary target but with 15 already on the board, they can at least approach games such as this one with little to lose and everything to gain. They have plenty of breathing space over the bottom three.
1.58pmRESULT! The final whistle goes at Vicarage Road and Stoke have held on to record an impressive 1-0 victory over Watford. It's a result which sees them move above Bournemouth into 10th place in the table. Fancy seeing what happened? Have a read of our on-the-whistle match report.
2.03pmGoing back to Arsenal and this match was one that Wenger could have potentially used to rest Alexis Sanchez. He's had a hectic schedule of late and is known to be carrying a slight hamstring injury but he has been preferred to Giroud, who has scored a few goals in recent matches. Wenger will argue that Sanchez will be rested for the EFL Cup in midweek but if he rested him today as well, he could have had his "Christmas break" early and be refreshed for the run of games coming up. That's my theory anyway...
2.07pmPREDICTION! It's prediction time! While Arsenal have been average in their last three games, they are huge favourites to run out comfortable winners this afternoon and we are backing them to do exactly that. We think Bournemouth will pose a threat on the break but Arsenal should be too strong. The Gunners to prevail 3-1.
2.10pmA quick look at our Stat Centre will show you that Bournemouth have only conceded four more goals than Arsenal this season. You associate Bournemouth with a pacey attack and limited defence but it has been the other way around during the first three-and-a-half months of the season. It will be interesting to see how this one pans out if Bournemouth can frustrate Arsenal during the early stages...
2.13pmThe two teams are out at the Emirates Stadium. It's a bright but chilly day in North London. Let's hope the football warms everyone up!
1 minWe are underway. Arsenal are straight into possession...
2 minCHANCES! Ake has just kept Bournemouth on level terms. It appeared that Ozil only had to slot home from 12 yards but the on-loan Chelsea player slid in to make the block.
After that, Bournemouth broke up the other end of the pitch but Adam Smith's 25-yarder went wide of the post. A lively start.
4 minBOOKING! That's an easy decision for the referee. Cook goes sliding in on Sanchez but he gets nowhere near the ball.
6 minIt's been an even start at the Emirates Stadium. Arsenal have had that chance and a free kick to the left of the penalty area but Bournemouth are wasting no time in getting forward.
7 minBOOKING! Talk about making things difficult for yourself. Francis now goes into the book for a very por challenge on the advancing Oxlade-Chamberlain. That's two of Bournemouth's defenders who are already on a yellow card.
9 minFrom the free kick, Elneny was found on the edge of the penalty area but after taking a touch, Ake was able to make another stunning block to deny what was probably a certain goal.
12 minWe have a late entry for the bloopers of 2016 DVD which will be in all recognised retail stores next week. Cook has had an absolute nightmare. He tried to pass the ball to Federici but it had nowhere near enough pace and it went to Sanchez, who passed the ball into the net from the edge of the penalty area.
16 minSUBSTITUTION! Oh no! Debuchy has suffered an injury and is having to be replaced by Gabriel Paulista. His first appearance for the Gunners in over a year and it's lasted 16 minutes.
20 minArsenal are well on top now but Bournemouth are still giving it a go when they get the ball in the final third. A Brad Smith shot nearly gets deflected into the path of a teammate before Wilson is nearly found inside the penalty area.
23 minBournemouth equalise from the spot! It comes after Monreal is adjudged to have barged over Wilson in the box. It could have been seen as a 50-50 but the referee decided that Monreal was the aggressor. Wilson stepped up to send Cech the wrong way.
25 minCHANCE! Bournemouth should be ahead! Huge, huge chance for Adam Smith. Ake's header back across the box found his teammate but he sent his free header from eight yards over the bar! Before that, Koscielny was extremely fortunate to avoid at least a yellow card for a bad tackle on Arter.
28 minCHANCE! Bournemouth are really going for this! Brad Smith is found inside the area but instead of passing the ball across for Wilson, he attempts to find a gap at the near post but his shot is saved by Cech.
32 minEverything has now calmed down to a certain extent. It looked like tensions were beginning to boil over but both sides are now focused on trying to play football than pressurise the officials. Bournemouth are the better team still, however.
36 minWilson is doing a really effective job in leading the line for Bournemouth. He's pulling Mustafi and Koscielny into the wide areas and he always looks like he has the pace to beat them in a one-on-one duel. If he can play like this on a regular basis, the big teams in the Premier League will be knocking on Eddie Howe's door.
38 minCHANCE! Better from Arsenal, and from Sanchez who comes alive in the penalty area. However, after a quick one-two, his volley goes several yards over the crossbar when he should have at least tested Federici.
42 minThis is an important period for Bournemouth. They have been the better team but they are on the back foot now. Walcott almost got a shot away inside the penalty area but several defenders got in the way. There was an appeal for handball but it would have been harsh.
45 minThere will be three minutes of added-on time.
45+3 minWOODWORK! Arsenal nearly snatch the lead back with a ferocious effort from Sanchez but his effort from 16 yards is tipped onto the crossbar by Federici. It's a stunning intervention.
3.04pmThe half-time whistle goes at the Emirates Stadium and we remain on level terms. Bournemouth have probably shaded it but Arsenal finished strongly and will have the momentum when we return for the second 45 minutes.
46 minWe are back underway. No changes from either side. That will change should Arsenal not find a second goal.
47 minWe haven't seen much of Ozil but his inswinging free kick has just nearly led to a goal. Unfortunately for Arsenal and the German, no-one could get the decisive touch at the back post.
50 minArsene Wenger has got someone to zip up his coat at the break. That's how you know he's serious. His team have bossed the opening five minutes of this half.
53 minWenger looks far happier now. The goal had been coming and it's an excellent team goal which has given Arsenal the lead for the second time in this match. A first-time cross from Monreal found Walcott at the back post and the winger has the relatively simple task of heading into the net from around four yards out.
57 minIt's worth noting that we are yet to see Xhaka in any kind of disciplinary trouble this afternoon. He's had criticism for that area of his game but he has kept his nose clean...so far.
60 minIt seems a matter of when, not if, Arsenal score a third. They perhaps should have done on this occasion when Xhaka released Sanchez but the Chilean's pass towards Ozil was hit too hard and Federici was able to claim.
62 minBOOKING! Controversial moment here. Sanchez lunges into a tackle with Arter and his studs goes down the Bournemouth's player Achilles and his ankle jerks back. Arter is up but that should be a red card for Sanchez.
63 minSUBSTITUTION! Arsenal give a warm reception to Afobe, who has been introduced for Bournemouth with Wilson (!) going off. Strange decision from Howe. He didn't appear to be injured.
67 minBournemouth are starting to press for an equaliser but they don't carry the same threat which troubled Arsenal in the first half. That said, it's probably down to Wenger allowing his players to sit deeper. Everyone is behind the ball at the moment, even Sanchez.
70 minSUBSTITUTION! Bournemouth are being forced into another alteration with Stanislas having picked up a calf problem. Jordan Ibe is the man to come on in his place.
73 minBOOKING! Should Bournemouth have had a penalty here? Arter thinks so but the referee doesn't. It leads to Arter being booked for dissent. The ball was flicked up and it hit Monreal's arm but that would have been a soft penalty.
75 minSUBSTITUTIONS! Double substitution for Arsenal as Wenger introduces Ramsey and Giroud for Oxlade-Chamberlain and Walcott.
77 minCHANCE! It's nearly a fairytale return for Afobe who reacts instinctively to meet a flick on from a corner but Cech is able to pull off a fantastic save from point-blank range. Big let-off for Arsenal.
80 minBOOKING! Brad Smith goes into the book for another late tackle from a Bournemouth player and it's his last act as he is replaced bu Lys Mousset.
85 minBournemouth are still probing for an equaliser but Arsenal have tightened things up at the back. It's probably going to take a moment of genius or a mistake for the Cherries to get back into this one.
88 minBOOKING! Gosling becomes the fifth Bournemouth man to go into the referee's book. The visitors have been very reckless today.
90+1 minGame over. Ozil plays in Giroud, who reaches the byline before crossing for Sanchez to slot into an empty net. Just before that, Mousset had headed wide for Bournemouth under pressure from Monreal.
4.11pmThe full-time whistle goes at the Emirates Stadium and Arsenal have been able to seal the win that takes them back to within three points of Premier League leaders Chelsea. The result is slightly harsh on Bournemouth who had their moments in North London but they were made to pay for not taking their chances.
4.12pmThat will be all from Sports Mole for this game. Thank you for joining us this afternoon and we hope that you can stick around for the game between Manchester United and West Ham United, which gets underway in just over 15 minutes time. Goodbye for now.