Ameobi, in the Magpies side as a replacement for injured top-scorer Andy Carroll, pounced in the 19th minute when Ali Al Habsi blocked Joey Barton's shot and Peter Lovenkrands's follow-up hit the upright.
Fabricio Coloccini and Steven Taylor also both struck the woodwork for the visitors, while Gary Caldwell saw his header come back off the bar for the Latics.
It was a welcome start to 2011 for Alan Pardew as his side bounced back from two straight defeats and moved up to 10th place.
For Wigan, who are just a point and a place above the relegation zone, the situation is more concerning.
Newcastle created the first goalscoring opportunity after just two minutes as Danny Simpson swung a cross into the box from the right.
Ameobi was allowed the space to meet it but the striker was unable to find the target, heading the ball back across the face of goal.
Three minutes later Wigan went close themselves as a failed clearance from Ben Watson's free-kick fell to Tom Cleverley, whose curling shot drew a smart save out of Steve Harper. Antolin Alcaraz headed the resulting corner straight at the Magpies goalkeeper.
Cleverley was presented with another chance on the quarter-hour mark after receiving a neat pass from Mohamed Diame, but the on-loan Manchester United youngster volleyed over the bar.
It was encouraging stuff from the hosts, but within moments, they were behind after a defensive error by Steven Gohouri.
Having dispossessed the Ivorian, Barton struck an effort which Al Habsi managed to parry, but Lovenkrands hit the loose ball against a post and Ameobi was on hand to tuck away the rebound.
An unmarked Lovenkrands should have doubled his side's advantage in the 31st minute after Barton squared to him right in front of goal, but the Dane got the ball stuck under his feet and Watson rushed in to avert the danger.
At the other end Cleverley's deflected shot from the edge of the box earned Wigan a corner which was met by Caldwell. The Latics skipper saw his header bounce back off the bar and the ball came to Hugo Rodallega, who lifted his attempt over.
Newcastle were next to hit the woodwork soon after as Coloccini looped a header onto the top of the goalframe and then Al Habsi had to be alert in rushing out to halt Jonas Gutierrez's progress.
Lovenkrands nodded a good chance over from a cross by Barton, and the former Manchester City man sent a free-kick off-target just before the break.
Martinez substituted Hendry Thomas for James McArthur at half-time and Wigan made the early running after the re-start, Jordi Gomez advancing down the right side but sending his delivery into Harper's arms.
Rodallega tried his luck twice in quick succession only to shoot wide of the mark each time.
Mauro Boselli was then introduced in place of Gomez to give Rodallega fresh support in attack, but it was Newcastle who nearly scored 10 minutes later as yet another header hit the crossbar.
This time it was Taylor denied after he got on the end of Barton's free-kick.
Lovenkrands and Ameobi came off for Wayne Routledge and Leon Best as the visitors looked to close out the game.
Boselli claimed his shot had been blocked by Taylor's hand in the box, but referee Howard Webb waved play on.
The Yorkshire official, who had been made an MBE in the Queen's New Years Honours List, then booked Barton for a rash challenge on McArthur.
Newcastle might have added a second goal towards the end as first Best poked wide after finding himself through one-on-one and then Jose Enrique blasted over, but come the final whistle, they had done enough.