Arsene Wenger’s men looked set to drop two crucial points after Andre Gray converted from the spot, before the Chilean saved the day.
Arsenal moved up to second in the Premier League after downing Burnley 2-1 in a thrilling match on Sunday, despite being reduced to ten men.
The Gunners took the lead through Shkodran Mustafi’s header in the second half, before Granit Xhaka received his marching orders for a two-footed lunge on Steven Defour.
And Arsenal’s title hopes were on course to suffer a huge blow when Andre Gray scored a penalty after Francis Coquelin fouled Ashley Barnes inside the box.
However, Ben Mee soon gave away a penalty for a foul on Laurent Koscielny and Alexis Sanchez saved the day by beating Tom Heaton.
Arsenal, now five points behind leaders Chelsea – who face Hull City later on Sunday – have an FA Cup tie away to Southampton and league game against Watford to come before a crunch meeting with the Blues at Stamford Bridge on February 4.
Burnley, meanwhile, stay 13th, having gone unrewarded yet again for a determined showing, as home form continues to be the most likely method of securing top-flight status for last season’s Championship winners.
The Clarets fans who made the journey to the capital could be forgiven for not recognising their team in the first half. Burnley had lost eight of their nine previous league matches on the road this season, but they were unexpectedly defiant during the opening 45 minutes in London.
A 0-0 draw at Manchester United in October was the only prior occasion Burnley had returned from an away game with anything to show for their efforts and perhaps another heavyweight engagement inspired Sean Dyche’s men to raise their level. Goalkeeper Tom Heaton proved equal to the task when called upon to make saves from Mesut Ozil, Koscielny and Sanchez.
The Gunners continued to dominate and they were rewarded a minute before the hour mark, Mustafi beating Stephen Ward to the ball from Ozil’s corner and heading into the far side-netting, beyond the reach of the stretching Heaton.
Given Burnley’s struggles outside the home comforts of Turf Moor, that goal initially appeared potentially fatal to the visitors’ chances, until Xhaka earned a straight red card for a lunging, studs-up challenge on Defour.
The away team had toiled without reward as they attempted to trouble Cech, a cause not helped by the worrying sight of Marney being stretchered off with 15 minutes to go.
Gray would later benefit from Coquelin’s rashness in the 93rd minute, but Mee then committed a reckless infraction of his own.
Wenger had to celebrate Sanchez’s dramatic winner out of the limelight, having been sent off by referee Jon Moss during a thrilling, fractious climax, which ended with Dyche as the wronged party, the Burnley boss angrily confronting the fourth official as another away point slipped out of his team’s grasp.