The Spaniard dispatched his spot kick past Wigan goalkeeper Ali Al-Habsi after 60 minutes following Theo Walcott's tumble in the penalty area under a clumsy challenge from Jean Beausejour.
Arsenal's third consecutive Premier League victory moved them above Tottenham Hotspur and Chelsea onto 30 points from 18 games although Tottenham can move back above their north London rivals if they beat Stoke City later.
Chelsea face Aston Villa on Sunday.
Wigan, third from bottom, had the best chance of a poor first half when Arouna Kone sprinted through on goal but dragged a left-footed shot wide.
Arsenal were more lively after the break and Walcott, who is still to sign a new contract for the club, was denied by Al-Habsi after he was picked out by Alex Oxlade-Chamberlain.
Wigan's response was impressive and they forced Arsenal into some desperate defending on a rain-sodden pitch.
Kone had another chance but was denied by Arsenal's Polish keeper Wojciech Szczesny and Dave Jones thumped a shot narrowly wide of the upright with Szczesny rooted to the spot.
Arsenal held out, however, to put some pressure on their rivals for a top-four place.
Later on Saturday, Manchester City can close the gap with leaders Manchester United to three points when they host bottom club Reading. (Reporting by Martyn Herman, editing by Mark Meadows)
- Sports & Recreation
- Theo Walcott
- Tottenham Hotspur
- Arouna Kone