The visitors dominated the first period but were dealt a severe blow on the stroke of half-time when Ryan Borris was shown a straight red card for allegedly head-butting Arbroath defender Kevin McMullan.
Borris and McMulllan both felt the decision was harsh. "I was astounded," Borris said after the match. "The linesman told the referee that I'd head-butted the Arbroath player and, although I put my head close to his, I never touched him."
McMullan agreed, saying: "There was a bit of jostling between the two of us, but nothing too serious."
David Bagan had gone close to giving Dumbarton the perfect start but his 20-yard shot in the second minute was pushed over the bar by Mark Peat.
The visitors continued to press, forcing a succession of corners while Arbroath were restricted to the occasional breakaway.
Peat was the home side's saviour again in the 13th minute when he brilliantly tipped a powerful Chris Hamilton header onto the bar.
Marc McCulloch twice threatened to give Arbroath the lead with free-kicks, the first being saved by Stephen Grindlay, the other hitting the side-netting.
Arbroath enjoyed a greater share of the possession in the second half but couldn't take advantage of having the extra man and Dumbarton continued to look dangerous on the breakaway.