Barry Douglas, Conway and Swanson netted as United climbed into fifth place in the Clydesdale Bank Premier League, with Josh Magennis replying for the Dons.
Conway and Swanson were each substituted in the second half as Houston had one eye on a packed programme - Monday's match was the first of five for United in 12 days.
"I've always said if I can get Conway and Swanson on the park at the same time we'll cause teams problems and we did cause them problems," said Houston.
Houston is poised to rotate his squad, with players returning to fitness to boost his resources - including Mihael Kovacevic, who was in the squad for the first time since the Scottish Cup win at Hampden last May.
"We want the points and we need the points to make sure we consolidate in a top-six finish," added Houston. "I've not got a massive amount of players to change it that much, but certainly we'll have to use in the next couple of days the full squad."
Source: PA
Source: PA