The Bolton defender steered home a rebound after Barnsley goalkeeper Luke Steele had spilled Marcos Alonso's vicious free-kick, giving Dougie Freedman's side their first away win in the league since the end of November.
It was cruel on Barnsley, who had fought back from two goals down at half-time to draw level early in the second period, but their survival hopes have been dented by a second successive defeat.
David Ngog and Jay Spearing fired Bolton into a deserved two-goal lead before Barnsley hit back 90 seconds into the second period through Tomasz Cywka and equalised in the 53rd minute when Chris O'Grady converted from close range.
But Bolton regained the lead six minutes later through Dawson and the visitors stood firm, recovering their composure in the closing stages to give their play-off challenge some momentum.
Bolton scored with their first attempt in the 15th minute when Chris Eagles pounced on a defensive mix-up inside the penalty area and teed-up Ngog, who despatched a volley from 12 yards into the bottom corner.
The visitors possessed that extra bit of quality and both Eagles and striker Craig Davies, back at Oakwell for the first time since his £300,000 move to Bolton in January, curled shots just off target before Bolton deservedly doubled their advantage in the 38th minute.
Barnsley only half-cleared the ball on the edge of their area and Spearing drilled home a low shot from 25 yards beyond Steele.
Barnsley made the perfect start to the second half with Cywka curling home a fine goal inside 90 seconds. O'Grady slipped the ball to Cywka on the right edge of the area and the Pole bent his right-footed shot inside Adam Bogdan's far post.
The Tykes were back on level terms in the 53rd minute. Ryan Tunnicliffe, on loan from Manchester United and making his home debut, played the ball in from the right across the face of goal to isolate Bogdan and O'Grady side-footed the ball home from six yards.
Bolton were rocked into action and when Barnsley defender Martin Cranie fouled Ngog on the edge of the area, defender Alonso's subsequent free-kick was spilled by Steele and Dawson slammed home the rebound.
Barnsley swept forward from the restart and should have scored their third, but O'Brien fired his angled shot straight at Bogdan in a one-on-one and within seconds Eagles had two efforts cleared off the goalline in quick succession at the other end.
Tykes substitutes Jacob Mellis and Jason Scotland then fired shots from the edge of the area over the crossbar as Bolton were pushed on to the back foot, but David Flitcroft's relegation battlers ran out of steam towards the end and Bolton held on.