They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
Sanchez broke the deadlock in the 60th minute of what had been a cagey game, selling the Saints defence a dummy before finishing left-footed for his 20th goal of the season, before Giroud headed a second with seven minutes remaining.
Arsenal moved above Manchester United into fifth on 66 points, three adrift of fourth-placed Manchester City with both having played 35 games. Arsene Wenger's side will also hope to reel in Liverpool, who have 70 points from 36.