The visitors actually took the lead in the 26th minute when Portuguese midfielder Flavio Paixao got the better of Dundee skipper Scott Robertson in an aerial dual in the goalmouth following Simon Mensing's header from a Doug Imrie Corner.
However, David Goodwillie restored parity just before half-time at Tannadice Park with his 13th goal of the season when he hammered home from six yards.
A tight tussle ensued with the home side slightly shading the Accies and but the Arabs needed injury time to get the win when Goodwillie played a neat reverse pass to substitute Jon Daly who slotted home to wrap up maximum points.
Houston was delighted with the showing of Daly who was playing his first game in three weeks after undergoing hernia surgery.
"Jonny was feeling really good and doing all the running and working with the physio," Houston said.
"The physio and our doctor wouldn't give him permission until we spoke to the guy who performed the operation.
"He told Jon 'if you're feeling all right, get on with it'. Big Daly hasn't trained an awful lot for a few weeks but he was good for 20 minutes.
"And I feel his presence helped. He had been doing well and scoring goals before he went out. Goodwillie sets him up brilliantly but it's a good finish from him."