Jon Daly's penalty put the city derby beyond Dundee as United claimed another victory over their neighbours.
Daly was handed a second chance to beat Rab Douglas when referee Willie Collum penalised Gary Irvine for a foul on Stuart Armstrong after the Dundee United midfielder had cut the ball back for the Irishman to shoot into the goalkeeper's hands.
Daly made no mistake from the spot to put United two up in the 71st minute and Willo Flood wrapped up three Clydesdale Bank Premier League points in the latter stages when his weak effort bobbled over Douglas's arm.
Smith called for clarity over the advantage rule after Jon Daly's penalty, but Houston said: "I thought when you wipe someone out in the penalty box it's a penalty kick?
"Daly got a shot in but Armstrong didn't get the contact he wanted on the cross. He got wiped out.
"We have had it against us and today it went for us. The referee made the right decision and a brave decision."
Houston's team beat Dundee 3-0 in August in the first competitive Dundee derby for seven years and also triumphed by the same scoreline at Dens Park in a friendly in July.
"I think in recent games we have played better football but a derby match is all about winning and giving the supporters bragging rights," he said. "It was a professional performance. That's the third derby and it's three 3-0 victories so I can't ask for any more."