Swans boss Kenny Jackett made one change from the side that won at Walsall, with Trundle coming back to replace Paul Connor up front.
There were three changes in the Barnsley line-up following Saturday's home draw with Brentford.
McLeod opened the scoring in the 13th minute after the Barnsley defence failed to clear. The ball was worked back to the former QPR midfielder and he blasted his shot into the roof of the net from fully 20 yards for his third strike of the season.
He almost snatched a second seven minutes later when Trundle and Adebayo Akinfenwa worked the ball out wide, but his crisp shot skimmed past the far post.
The Tykes equalised in the 35th minute when Trundle failed to clear from just outside the home penalty area. Jacob Burns pounced on the loose ball and though Willy Gueret went down to save, it squirmed off his body and into the corner of the net.
Five minutes into the second half the busy McLeod crossed from the left and Akinfenwa just failed to get a touch from in front of goal.
The Swans took the lead in the 58th minute when Trundle won a free-kick 20 yards out, but in a central position. It took an age to push the Barnsley wall back, but when they were finally ready Trundle curled the free-kick into the top left-hand corner with keeper Nick Colgan well beaten.
A Barry Conlon back header deceived Gueret but struck the post before being hacked clear.
Akinfenwa and Trundle both missed gilt-edged chances in the closing minutes as Barnsley, now down to ten men after using all three subs and losing Stephen McPhail through injury, were pinned back on defence.
McLeod scored his second in the 88th minute to clinch the three points with another crisp drive that beat the shell shocked Barnsley keeper all ends up.
The victory, following on from Saturday's success at Walsall, lifts the Swans up to second place in League One.