Centre-back Collins opened the scoring by poking past keeper Ross Worner at the far post after latching on to Darren Carter's lofted free-kick.
And a solo effort from Dallas sealed the win with 16 minutes remaining as Northampton won for the first time in nine games, while ending Wimbledon's 100% home record.
Despite not having the lion's share of possession, Northampton had the best opportunities in the first half and went ahead when 25-year-old Collins found himself unmarked following Carter's free-kick to fire home a 20th-minute opener.
Ian Morris sent an unmarked header over two minutes after Collins' opener and Gary Deegan had a half-volley disallowed after it deflected into the net off an offside team-mate.
A deft strike from Michael Smith almost levelled the scores in the 60th minute, but his curled effort was inadvertently blocked by George Porter.
But Northampton doubled their lead after 74 minutes as winger Dallas took the ball around left-back Jim Fenlon and calmly slotted past Worner at the near post.
A diving save from Northampton keeper Matt Duke denied Harry Pell an injury-time consolation.