Di Santo opened the scoring with a superb right-foot finish five minutes before the break and added his second after 66 minutes when he looped a deflected shot over Paddy Kenny.
The visitors had chances themselves in a bright game and Adel Taarabt hit the post twice in the first period, but Roberto Martinez's men ran out worthy winners.
Most of the home side's purpose was inspired by Hugo Rodallega, making his first Premier League start of the season after returning from Copa America duty with Colombia.
Rodallega's trickery won the fourth-minute free-kick which Jordi Gomez squeezed over the bar, then he skipped round Bruno Perone to fire across the face of goal.
In a bright opening, the visitors had their first chance in the 10th minute when Shaun Derry blasted a long-range effort which was tipped over the bar by Ali Al Habsi.
And Rangers had a glorious chance after 14 minutes when Akos Buzsaky fed Taarabt, whose right-foot shot rebounded off the post to the clear but unprepared Patrick Agyemang, who squirted it wide.
The visitors had another chance in the 25th minute when Alejandro Faurlin found Buzsaky on the right and his cross was met at the far post by Perone, who headed over.
A quick counter-attack by Rodallega almost paid off in the 37th minute when he squeezed the ball out to Victor Moses who cut in from the right and hit a low shot straight at Paddy Kenny.
Wigan broke the deadlock five minutes before the break, when the superb Rodallega squared for Di Santo who wasted no time slamming the ball into the net.
Rangers hit the woodwork for the second time in first-half injury time when Taarabt's long-range free-kick deceived Al Habsi but rebounded for Mohamed Diame to clear.
The second half started with much the same sense of urgency but fewer clear-cut chances as the Wigan midfield did a good job snuffing out Rangers' bid for an equaliser.
The home side had the first clear-cut chance in the 58th minute when Moses found Gomez on the left and the midfielder's shot from a tight angle was deflected out for a corner.
Moments later, Di Santo came close to his second goal from an almost identical position, drilling a rising shot which was well saved by Kenny.
Di Santo finally grabbed his and Wigan's second after 66 minutes when he turned and shot from just outside the box and the ball took a slight deflection as it looped over Kenny.
The visitors refused to give up on the afternoon and came close when Perone connected with a Taarabt corner in the 75th minute to bring a fine save out of Al Habsi.
Taarabt then forced another fingertip save out of Al Habsi from an excellent free-kick after Latics captain Gary Caldwell brought down Agyemang.
Boyce booted clear a dangerous cross by Bruno Andrade then Agyemang ought to have done better in injury time but shot wide when clear in the box.
But while the final whistle brought joy for Wigan it also put Barton's arrival in sharp perspective with Rangers clearly needing his input to boost their survival bid.