The Tannadice club dismantled their opponents to book their place in the fifth round of the William Hill Scottish Cup thanks to a Johnny Russell hat-trick and a brace from Jon Daly.
Houston said: "It was a complete performance against a plucky Stranraer side.
"They worked very hard against us and it is not every day that they will play against a team like Dundee United.
"It was a hard one for them and if some of their young players learn from today then they have done well."
Houston added: "The most important thing is being in the next round of the cup.
"I hear Arbroath scored a late goal against Celtic and that is the kind of thing that can happen in cup football.
"Stranraer is a long journey - four and a half hours from Dundee on Friday - after Ayr it is quite hazardous but the boys were switched on today.
"I think that is the biggest thing; making sure they were switched on and knowing they were going to have win the battle."
Russell opened the scoring after 13 minutes when Barry Douglas' through ball was deflected into his path.
The striker then found the smallest of gaps to fire the ball home between David Mitchell and the near post.
Douglas was involved in the second goal just before the half hour when his cross found Rudi Skacel.
The ex-Hearts man, who lifted the cup last year, turned inside and picked out Russell who again put the ball in the back of the net.
There was still time for Russell's strike partner Daly to find the net before the break.
This time Russell turned provider as he held the ball up for Daly to fire home from close range.
Daly took his tally to two just after the hour mark when he swept home from a corner after Stranraer failed to clear their lines.
Russell took the match ball as he added number five with 21 minutes left on the clock.
This time it was the goal of the game as Mitchell did well to deny Stuart Armstrong's low shot only for it to spill to Russell on the edge of the box.
The striker kept calm to sweep the ball home and secure United's place in the next round.
The striker could have scored a fourth right at the death when he broke through only to see his low shot blocked by Mitchell at the expense of a corner.
Stranraer manager Stevie Aitken praised the visitors for their professional attitude.
"To be fair to Dundee United, they came down with a great attitude," he said.
"Sometimes it is difficult for big teams to come to a place like this and maybe they do not show the right attitude but fair play to them.
"They made it difficult, they made it hard, which was always going to be the case but my players gave everything."