Peter Crouch set up a potentially nervous finish with a 66th-minute goal -- though replays appeared to show the ball going in off the forward's hand -- but Sanchez and Giroud, with his second, sealed an impressive victory with scores in the 76th and 80th minutes.
With two matches remaining, Arsenal, winners of five of their past six games, have 69 points -- one fewer than Liverpool in fourth. Stoke, who have won just one of their previous 10 league games, sit in 13th with 41 points.
"We were efficient up front and defensively were compact and defended well from the front," Giroud told Sky Sports.
"It's a great win and we've got two more finals to come.
"The most difficult thing against a team like Stoke is scoring the first goal and after that we had to be efficient.
"West Ham have all my support against Liverpool. We have to do the job first and see what happens, we'll keep fighting until the end."
Arsenal host relegated Sunderland and Everton in their remaining games while Liverpool visit West Ham United before playing Middlesbrough on the final day.
Manchester City, third with 72 points, face West Bromwich Albion and Watford.
(Reporting By Tom Hayward, editing by Pritha Sarkar, Neville Dalton)
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