Stoke controversially restored hope as Peter Crouch converted Marko Arnautovic's cross with his hand, but Sanchez drilled in a low finish and Giroud slid in a fourth for the away side. Both Arsenal and Liverpool have two games remaining and are level on goal difference with the Gunners ahead by one on goals scored. Jurgen Klopp's men travel to West Ham on Sunday (kick-off 14:15 BST) and play Middlesbrough on the last day of the season, while the north London club host Sunderland on Tuesday and Everton in their final league match next weekend.
Wenger's season has been blighted by protests demanding he end his long association with the club, repeated questions over whether he will sign an extension to his contract, which runs out at the end of the season, and uncertainty over the futures of key players Sanchez and Ozil. But he will be pleased with the way his players have responded with the campaign coming to a close, taking five wins from their past six league games - the only blemish a weak display in their defeat by Tottenham. He was even afforded a standing ovation at full-time and will be particularly satisfied at triumphing at a venue where his side have struggled in the past, claiming their first win there since 2010. Wenger jumped off his seat and jigged in delight at Sanchez's goal, which gave his team a cushion.
The Chilean, who has been linked with a move away, hobbled off with a leg injury after scoring and fans will be hoping it is not the last time they see him in an Arsenal shirt. A season that promised so little at one stage could actually turn into a celebratory one. Their late charge sees them maintain optimism of extending their Champions League participation to 22 consecutive seasons, and they have an FA Cup final against newly crowned Premier League champions Chelsea to look forward to. Stoke's season is petering out with a whimper - they have won just one of their past 10 league games. This loss means they will finish in the bottom half for the first time since 2012-13 - their worst season in the Premier League as they finished 13th with 42 points.
Although the Potters are in the same position at the moment, they have one fewer point and will be hoping to win their last game of the season at Southampton to end on a high. Even after pulling a goal back against Arsenal - which should not have stood after Crouch's handball - Stoke did not look like getting anything out of the game with Mame Biram Diouf summing up their performance by nodding wide from just three yards out.