The Chilean scored a pair of goals, continuing his tremendous form against the Premier League's bottom side.
Alexis Sanchez continued his hot streak in front of goal as his brace inspired Arsenal to a 3-0 victory over winless Burnley.
Arsene Wenger's men had failed to collect a Premier League win on home turf since the opening day against Crystal Palace and they appeared set for another afternoon of frustration against the bottom side in the division.
The former Barcelona man sparked relief around the Emirates Stadium in the 70th minute. Impressive right back Calum Chambers crossed for Alexis to score with a header, and the teenager added a second himself two minutes later with his first goal in senior football.
Alexis fashioned space from Kieran Gibbs' low center to net a 10th goal in 12 appearances in the final minute and add gloss to the scoreline, as Arsenal moved above West Ham into fourth, while Burnley is three points adrift at the bottom and five from safety.
Arsenal was unchanged from the team that beat Sunderland last weekend, while Burnley recalled midfielder Dean Marney following a hamstring injury and striker Marvin Sordell.
The hosts dominated possession but made little impression on Burnley until Kieran Tripper produced a vital clearing header to deny Danny Welbeck in the 21st minute after Alex Oxlade-Chamberlain had raced away down the Burnley left.
The visitors enjoyed a rare foray into the opposition penalty area 31 minutes in, only for Mathieu Flamini to make an important interception by prodding Scott Arfield's pass away from Danny Ings.
Alexis then twice went close, first cutting in from the left and forcing Tom Heaton to push away his rasping drive before arching another 25-yard effort narrowly past the right-hand post.
Heaton proved Alexis' equal once more when the livewire forward raced into the box five minutes before the interval, as Burnley managed to reach the break unscathed.
Ings was unable to capitalize on a moment of confusion between Arsenal goalkeeper Wojciech Szczesny and Per Mertesacker in the 50th minute as Sean Dyche's men made a more assertive start to the second period.
Michael Duff produced some remarkable defensive heroics for the visitors as he flung himself to ground to deny Cazorla with the goal gaping after Chambers' cutback.
The pressure eventually told, though – almost inevitably from the Burnley left – as Alexis got ahead of Trippier to net a fine header from Chambers' cross.
The creator then became the scorer two minutes later, with Chambers on hand to steer home after a combination of Heaton and David Jones had denied Welbeck.
The Arsenal faithful warmly welcomed back Theo Walcott from his lengthy injury absence soon afterwards and the England man and fellow substitute Lukas Podolski drew magnificent saves from Heaton in the closing minutes as Burnley’s resistance faded, allowing Alexis to have the final word with a third goal.