Scott McDonald hammered home a late winner to give the Tangerines a very welcome win at Tannadice.
The home team took the lead on 65 minutes thanks to a well-worked goal from James Keatings.
However, Morton hit back via a tap-in from substitute Bob McHugh 10 minutes later.
With just seven minutes left, however, striker McDonald smashed the ball home from close range after a Mark Durnan header had hit the post.
The result put them them second behind leaders Dunfermline and, while no one at the club will be getting carried away, this performance was an improvement on those produced in recent weeks.
The Tangerines made two changes to the line-up that started the goalless draw against Falkirk – one enforced and one tactical.
With defender Paul Quinn having been hospitalised after suffering a heart scare, his replacement from last Saturday, William Edjenguele, started the match.
The other alteration was frontman Keatings in for midfielder Sam Stanton, with the former Hearts, Hibs and Hamilton player recovering from a dead leg to start in attack alongside McDonald.
After a quiet start, United broke forward on 15 minutes but Billy King’s low ball across the face of goal was cleared.
The away supporters had optimistic shouts for a penalty rightly ignored by referee Alan Muir after Robert Thomson’s shot blasted into the body of Lewis Toshney, winding the United right-back.
On 22 minutes, the hosts came close when Edjenguele, who had been up for a corner, got to a cross before keeper Derek Gaston. The loose ball fell to McDonald and his shot was deflected just wide.
Paul McMullan, who was looking a threat to Ton, then tried his luck from 25 yards and Gaston had to look lively to push it away for a corner. King took the setpiece from the right and Durnan glanced his header wide.
Toshney was replaced on 29 minutes by Stewart Murdoch then Fraser Fyvie wasn’t far away with a strike from distance as United settled into the game.
On 32 minutes, the Tangerines almost grabbed the lead following a nice move. Keatings played a one-two with McDonald and, when the wee Australian scooped the ball back his way, Keatings took it first-time and fired a shot past the far post.
Just a few seconds later, Keatings came even closer when his downward header, which was bound for the bottom corner, was clawed away by Gaston.
It was a good first half from a dominant home team but once gain they failed to find the back of the net.
Just a minute after the restart, United were on the attack again. This time Keatings fired in a shot that hit the side-netting.
Just after the hour-mark, Morton broke forward through Jai Quitongo and the striker looked favourite to beat sub Murdoch in a race. However, the home player was helped by his keeper Harry Lewis, who raced out to block the shot. Quitongo pulled his hamstring during the move and was replaced by McHugh.
Having survived that scare, the hosts took the lead with splendid goal on 65 minutes.
The move came on the left-hand side, with four of their forward-thinking men involved as King played the ball to McDonald. The Aussie picked out McMullan and his flick was blasted home by Keatings, despite goalie Gaston getting a touch.
Five minutes later and it was almsot two when Fyvie let fly from outside the box but missed the post by a foot or two.
However, the scores were level on 75 minutes.
Ross Forbes took a freekick from the right and it was headed at the back post by Ricki Lamie to the waiting McHugh, who tapped it over the line from a couple of inches out.
United brought on both Partick N’Koyi and Stanton on 80 minutes in a bid to inject more spark into their attack and it paid off.
In this game of football ping-pong, it was soon United’s turn to score again.
With 83 minutes on the clock, King crossed and defender Durnan looked certain to score but smashed his header against the base of the Morton post.
To the relief of United’s fans in general and Durnan in particular, McDonald hammered home the rebound for what turned out to be the winner.
Attendance: 5,569.
Dundee United: Lewis, Durnan, Toshney (S. Murdoch 29), McMullan, McDonald, King, Edjenguele, Robson, Keatings (N’Koyi 81), Briels (Stanton 81), Fyvie. Subs not used: Deniz, Flood, Allardice, Smith.
Greenock Morton: Gaston, T. Murdoch, O’Ware, Lamie, Doyle, Oliver (Armour 79), Forbes (Harkins 86), Quitongo (McHugh 62), Thomson, Tidser, Russell. Subs not used: Doohan, Tiffoney, McManus, Langan.
Referee: Alan Muir.
