When on-loan Benfica forward Rodrigo Moreno produced a delightful finish to put Owen Coyle's men ahead in the 54th minute, the stage was set for the Trotters to emerge victorious.
Wigan had already lost on-loan playmaker Tom Cleverley to injury in the 12th minute and saw goalkeeper Chris Kirkland carried off on a stretcher shortly after the hour mark.
Yet Roberto Martinez's side refused to lie down and earned a share of the spoils in the 80th minute when Stam stabbed home at the far post to claim his first Wigan goal and earn a booking for his celebrations in front of the visiting supporters.
Bolton mounted a late rally but Johan Elmander was denied by a superb save from substitute Wigan stopper Mike Pollitt before Fabrice Muamba blazed over from six yards.
Kirkland, back from a loan spell at Leicester, was given the gloves with Ali Al-Habsi being ineligible to face the Trotters under the terms of his loan.
Wigan's relegation plight was underlined when an early own-goal from Chelsea defender Jose Bosingwa put Wolves 1-0 up at Molineux, increasing the pressure on Martinez's men before they had even kicked off at the Reebok Stadium.
Yet the Latics did not seem fazed in the slightest.
Kirkland - making his first start for Wigan since facing Bolton in the corresponding fixture at the DW Stadium on October 23 - claimed an early cross from Matt Taylor with calm assurance.
Moments later Elmander's delightful flick set Taylor into space inside the left channel but his low cross was well blocked by Antolin Alcaraz.
Wigan were then dealt a major blow when Cleverley, on loan from Manchester United, pulled up with what appeared to be a hamstring injury and was replaced by Mohamed Diame.
It was a severe blow to Martinez at such an early stage in the game but Bolton struggled to create genuine goalscoring opportunities as rain continued to fall.
Wigan's greatest threat came from Hugo Rodallega, who ploughed a lone furrow up front but showed enough quality on the ball to suggest he could pilfer a goal.
The Colombian frontman forced a fine save from Jussi Jaaskelainen in the 32nd minute when his fierce 25-yard free-kick was parried clear by the long-serving Finn.
Bolton held the upper hand without ever producing the skill required to unlock the Latics' dogged defence.
The Trotters went close twice within the space of as many minutes in similar circumstances shortly after the restart.
In the 47th minute Taylor's free-kick from the right was greeted by a powerful header from Gary Cahill but his effort flew just wide.
Then a corner from Taylor, again from the right flank, was completely missed by Kirkland and Cahill headed over from the edge of the six-yard box.
The Trotters began to dominate and broke the deadlock in the 54th minute when a delightful passing sequence led to Mark Davies spotting Rodrigo making a diagonal run inside the Wigan penalty area.
Rodrigo took a touch to steady himself and then clipped a superb left-foot shot past Kirkland from the edge of the six-yard box for his first goal in Bolton colours.
Bolton pressed for a second and after Elmander caught Kirkland with a late challenge, the goalkeeper required lengthy treatment before being carried off on a stretcher and replaced by Pollitt.
Yet Wigan refused to lie down and were level in the 80th minute with a goal that was testament to their proud passing game.
Rodallega found right-back Steve Gohouri advancing at pace down the flank and his low first-time cross was sidefooted home at the far post by the onrushing Stam.
Stam was booked for rushing towards the celebrating Latics fans but Bolton came back strongly in search of a winner.
They peppered Pollitt's penalty area with a series of teasing crosses but the veteran stopper made a superb stoppage-time save to repel Elmander's 12-yard drive before Muamba blazed wastefully from close range.