Last season's leading scorer headed United in front after just six minutes and his deflected effort before the hour mark put the seal on a controlled display.
After a mixed pre-season, in terms of results and performances, new boss Moyes will be satisfied to claim a piece of silverware in such straightforward fashion after Wigan failed to turn up.
United took the lead through the first chance of the game on six minutes. Van Persie spread the play to the left and the Dutchman's subsequent run was not tracked as he arrived in the penalty area to guide Patrice Evra's cross inside the post.
Wigan struggled to carry a threat going forward and had to remain alert at the back as summer signing Leon Barnett did well to cut out Wilfried Zaha's low cross at the near post.
The Premier League champions were forced into an early reshuffle on 16 minutes when Rafael went off injured to be replaced by Chris Smalling, who slotted in at centre-half, with Phil Jones switching to right-back.
The 2013 FA Cup winners finally threatened 10 minutes before half-time when new recruit James McClean flashed the ball across goal after Smalling had misjudged the bounce from a hopeful pass.
United created a rare opening on 38 minutes when Danny Welbeck turned and shot following Tom Cleverley's pass, but Wigan keeper Scott Carson parried the ball to safety.
A minute before half-time, Wigan created a flutter in the United defence when Emmerson Boyce headed Ben Watson's free-kick back across goal, but the ball was a fraction too high for Barnett.
The second half maintained the same low-key tempo which characterised the first, with United again creating the first chance as Cleverley scuffed his shot from the edge of the area after Zaha and Welbeck had combined.
Just before the hour mark, United extended their lead as Evra, Cleverley and Welbeck helped to work the ball from left to right to Van Persie, whose shot deflected off James Perch and left Carson with no chance.
United veteran Ryan Giggs was given a standing ovation when he was replaced by Anderson midway through the second half and substitutions from both sides in the closing 20 minutes failed to inject any spark into the game.
Evra was always a positive outlet on the left for United and Moyes will have been content with the control his team displayed ahead of next weekend's Premier League opener at Swansea City.
Wigan, meanwhile, struggled to put a cohesive move together and will now turn their attention back towards winning an immediate return to the top flight when they travel to Bournemouth in the Championship.