The Gunners should have been out of sight by half-time, but had only van Persie's 21st-minute strike to show for their dominance as Latics goalkeeper Ali Al Habsi made a string of fine saves.
The in-form Dutchman eventually fired in a second just before the hour, but then blasted a penalty over the bar after Gary Caldwell had been sent off for pulling back Cesc Fabregas.
However, Van Persie duly completed his hat-trick with five minutes left to make it six in the last three games.
Arsenal - with five changes from the starting XI that beat Leeds in their FA Cup third round replay on Wednesday night - started brightly.
Wigan keeper Al Habsi had to be alert as he got down quickly to save Samir Nasri's shot on the turn.
The Omani then produced a simply stunning one-handed block to palm away a point-blank shot from Van Persie.
Wigan were in danger of being overrun, but to their credit the visitors continued to try to go on the offensive themselves.
Walcott dashed to the goalline and pulled the ball back for Fabregas, who looked set to open the scoring, only for Caldwell to produce a superb block.
Arsenal eventually took the lead on 21 minutes after more patient build-up.
Alex Song released Van Persie, who was just onside, into the left of the penalty area - and the Dutchman fired in his fourth goal in three games.
Wigan continued to be pressed back in their own half. However, Arsenal could not make the most of possession.
Al Habsi denied Fabregas with another fine save before Maynor Figueroa made a last-gasp tackle just as the skipper looked set to slot the ball in at the near post.
Arsenal should have been 2-0 ahead when Walcott raced clear down the centre, but squared to Fabregas rather than try to round the keeper. Mohamed Diame made a saving tackle before Steven Caldwell threw himself of Walcott's follow-up shot from the loose ball.
Al Habsi tipped over a 20-yard drive from Nasri, then kept out Fabregas' low shot as the Gunners cut Wigan open time and again.
However, much to the frustration of the home fans, Arsenal were once again unable to turn their dominance into goals before the interval.
Wigan were much more competitive at the start of the second half following the introduction of Franco Di Santo, replacing Diame.
Slowly, though, the Gunners regained dominance as Walcott nipped into the right channel, but the angle was too high and his shot flew wide.
When the second Arsenal goal finally came on 58 minutes, it was simple, yet breathtaking.
Fabregas chipped a 30-yard ball over the defence, and Van Persie got ahead of Gary Caldwell to crash a left-foot volley past Al Habsi at the far post.
Jack Wilshere charged forwards, but then drilled a low shot wide from 20 yards.
Arsenal were awarded a penalty on 69 minutes when Gary Caldwell pulled back Fabregas in the six-yard box, and was shown a red card.
Van Persie stepped up for his hat-trick, but uncharacteristically blasted the spot-kick high over the crossbar.
The Dutchman almost made amends with a curling effort from 20 yards which struck the post.
Song's low shot from 20 yards flew just wide before Van Persie finally secured the matchball when he smashed home from a tight angle after Walcott had held the ball up in the penalty area.