Ashley Barnes converted Dean Marney's cross from close range to give the dominant hosts the lead.
Wigan striker Marc Antoine Fortune headed against the bar before Michael Kightly's free kick doubled the advantage.
Danny Ings hit the post for Burnley after the break before Latics forward Fortune headed wide.
Burnley, who had lost their last two home games, were promoted to the Premier League via the play-offs in 2009 but the last time they had earned automatic promotion to the top flight was back in 1973.
There was no stopping them on Monday as they dominated from the start to race into a 2-0 half-time lead. Wigan, who have been in great from themselves were poor.
The Clarets are now just four points behind leaders Leicester, who play their game in hand at Bolton on Tuesday and the title is still up for grabs.
The win means that Derby County, who beat Barnsley 2-1 are now confined to the play-offs.
Clarets boss Sean Dyche has only paid a transfer fee for one player since being appointed in October 2012 - buying Ashley Barnes from Brighton for £400,000 in January.
And it was Barnes who gave Dyche's men the perfect start, tapping home from close range after Marney's low cross from the left.
Wigan improved after the break and almost pulled a goal back when Fortune latched on to Jason Shackell's poor header, but his toe-poked effort was blocked by Tom Heaton.
It looks like the play-offs for Wigan.
Last time Burnley were promoted they stuck with many of the players who got them promoted under then boss Owen Coyle. That policy ensured that financially the club were in a sound position despite being relegated. Second time around you can expect a prudent approach in an effort to not get relegated straight away as they did last time.