The 19-year-old showed remarkable maturity in front of goal to steer his effort beyond West Brom goalkeeper Scott Carson and into the corner.
Moses had good cause for celebration in the 70th minute as it was his first league goal this season, although he found the target in the Carling Cup victory against Hartlepool.
It was a cool finish by the midfielder, who arrived from Crystal Palace at the end of January transfer window for £2.5million.
Wigan went into the match having scored only nine goals in 12 league games but with renewed confidence after drawing with Liverpool in midweek.
They almost made the breakthrough in the second minute following a deep cross from Ronnie Stam. He found Tom Cleverley in acres of space but the midfielder, on loan from Manchester United, saw his effort turned away on the line by Pablo Ibanez.
A minute later the visitors were pegged back again when striker Hugo Rodallega released Charles N'Zogbia inside the area but he stumbled and the move broke down.
Wigan were forced to make a change in the 17th minute when defender Gary Caldwell limped off and was replaced by his brother Steven, who arrived in the summer after playing for Burnley last season.
West Brom stepped up the pace and Peter Odemwingie raced to the byline in the 26th minute. He cut the ball back into the area but there was no-one on hand to take advantage and Antolin Alcaraz made the clearance.
Odemwingie was beginning to find a lot of room and broke free - only to send his powerful shot narrowly wide of the post.
Back came Wigan and Alcaraz escaped his marker in the 35th minute when N'Zogbia floated in a corner.
Alcaraz, however, only succeeded in sending a free header over the bar from a good position.
West Brom responded and seven minutes later and Steven Reid delivered a long throw into the area. Paul Scharner, back at his former club, flicked the ball on and James Morrison got a decent connection, only to see his effort deflected to safety.
Scharner then saw his shot blocked a minute before half-time after Wigan had failed to deal with a fine inswinging free-kick from Chris Brunt.
Moses came on at the start of the second half for Jordi Gomez and he quickly made an impact, racing away down the right. However, his cross in the 50th minute went behind the waiting N'Zogbia.
West Brom appealed for a penalty in the 55th minute when Caldwell tripped Odemwingie as he cut inside. Instead referee Anthony Taylor awarded a free-kick on the edge of the area and Brunt's effort came back off the wall.
Wigan made the vital breakthrough in the 70th minute through Moses - and West Brom went in search of the equaliser.
Steven Reid went close before the home side should have added a second goal in the 82nd minute. Substitute Franco Di Santo found himself clear on goal as Albion waited in vain for the whistle for offside - but he dragged his effort wide.
Marc-Antoine Fortune almost equalised at the end but Wigan goalkeeper Ali Al Habsi blocked his shot to leave West Brom frustrated.
The newly-promoted side are beginning to find it hard to win games after a bright start to the campaign.