Defender Leighton Baines gave Wigan a shock lead after only four minutes with a spectacular 25-metre drive and United needed nearly an hour before turning the game around with two goals in four minutes.
Serbian defender Nemanja Vidic headed home in the 62nd minute and France's Saha fired them in front with a deft control and shot in the 66th before Norwegian Ole Gunnar Solskjaer added a third in stoppage time.
United, who beat Wigan in February's League Cup final, fully deserved the win and will also be lifted by a fine display from England striker Wayne Rooney, previously struggling for form.
Alex Ferguson's men finished the game at the JJB Stadium three points clear of champions Chelsea, who were playing Reading in the day's late kickoff.
Wigan remain just goal difference above the drop zone.
Ferguson told Sky Sports: "Wigan are a difficult side to play against, they're very committed and they've got good balance to the team -- so I think we've done really well to come out with a victory.
"There's a good momentum about the team at the moment and hopefully we can keep that going."
Delighted with the performance from Rooney, he said: "Over the whole 90 minutes I think he was right back to his best -- he and Saha are a real handful. And of course, with Ryan and (Paul) Scholes's experience behind that, it always give you a chance."
Asked if it was Rooney's best United performance this season, Ferguson said: "I would think so.
"There were some signs of him coming back and even the two internationals have helped him get the required number of games to bring him to the right pitch."
A disappointed Wigan manager Paul Jewell said: "The first half took a lot out of us, but we can't sit deep. We were too easy to play against in the second half."
DREAM START
The hosts made a dream start when Baines, who scored with a 25-metre piledriver for England's Under 21s against Germany just over a week ago, repeated the feat after being teed up by a free kick.
United shrugged off the setback and Rooney produced a sharp turn and shot which smacked against the Wigan crossbar.
Saha was more successfully shackled by Wigan's defenders, but left back Patrice Evra managed to find room for a fierce drive just before halftime which keeper Chris Kirkland did well to block.
United kept pressing after the re-start, sharpened by the arrival of Ryan Giggs as a substitute, and Saha should have done better than firing wide after getting through on goal.
Vidic headed the equaliser soon afterwards, sandwiched by Wigan defenders but still able to meet Giggs's corner from the right with a powerful header.
Saha soon followed up by superbly controlling a high Rooney cross from the right and whipping the ball past Kirkland and in off the left-hand post.
Solskjaer, back in the goals after two injury-plagued years, stroked home his fourth league goal of the season after winning a challenge and finding the bottom right hand corner with a low shot.
