King cracked home the opener with just over an hour gone and then finished off an injury time breakaway to clinch the victory.
Laszlo said: “We created chances in the first half but didn’t score and that is our biggest problem as a team. However, we showed that we had character and that was really important to see. We were dominating the game but you have to score.
“It was a physical game as Morton have big and strong players, particularly up front, so I told my players to make sure they won the second balls and we did that really well.”
United created the game’s first opening on five minutes when Scott McDonald found Fraser Fyvie 25 yards out and the midfielder skipped past a retreating home defence before sending a shot across the face of Derek Gaston’s goal.
The Tannadice men threatened again on 13 minutes when Paul McMullan slipped a pass to McDonald, however Gaston was able to beat away the striker’s shot.
Quick thinking from Gary Harkins almost opened the door for Morton as his free-kick found Jai Quitongo, who sent a diving header across goal to the unmarked Robert Thomson, however Harry Lewis dived to cut-out the ball.
Another drive from Fyvie was spilled by Gaston but an offside flag ended McDonald’s attempts to score from loose ball.
The goal that the game deserved came just after the hour when McMullan fed King on the right of the box and the striker worked the ball on to his left foot before cracking in a low drive that flew past Gaston and just inside the post.
A poor Jamie Robson pass-back on 67 minutes gave Morton the chance to level and Quitongo slipped the ball past Lewis but it ran wide.
Another poor pass to Lewis, this time from Mark Durnan, almost let in Thomson but the shot-stopper ended the danger by sliding along the turf and heading clear.
Five minutes later, McMullan missed from less than a yard out and deep into injury time Fyvie led a breakaway after Harkins was robbed and he passed to King who slid the ball home with ease.
Home boss Jim Duffy said: “The score-line is harsh, however, the result was the correct one. We gave everything but they were a bit slicker.”