Dundee United put themselves in the driving seat in this Premiership play-off quarter-final with two classy goals at Cappielow.
They had to fight their way back after Morton took the lead on just seven minutes through a Thomas O’Ware header.
The Greenock men went on to boss the rest of the first half but a simply fantastic strike from Simon Murray – his 15th of the season – pulled United level five minutes into the second period.
Blair Spittal then fired a low shot home on 65 minutes to put the Tangerines 2-1 up. It was his third goal in four games and, boy, did he celebrate.
Both strikes were special and now United will head home to Tannadice on Friday night as firm favourites to go on and face Falkirk next week in the semi-final.
The Tangerines had made two predictable changes to the side that started at Cappielow on Saturday, with defender William Edjenguele and striker Simon Murray coming back after suspension to replace Coll Donaldson and Ali Coote.
The home team rang no fewer than five changes, with keeper Derek Gaston, Gary Oliver, Jamie Lindsay, Michael Tidser and Lawrence Shankland all coming in.
Backed by a noisy travelling support housed in two corners of the stadium, United got the game under way in glorious sunshine.
With just a couple of minutes gone, the visitors won a corner that was taken by Spittal and frontman Thomas Mikkelsen shot over the bar after the loose ball fell to him.
On seven minutes, though, United fell behind.
It was a poor goal to concede as Shankland sent over a long throw-in from the right and O’Ware headed powerfully past keeper Cammy Bell.
The Tannadice men tried to hit back and Mikkelsen’s low drive was saved by Ton goalie Gaston on 12 minutes.
Willo Flood lost possession inside his own half a couple of minutes later and Tidser raced on before smashing a 25-yard strike off the bar.
The game was being played at a frantic pace, with Oliver in particular giving United trouble up the right wing.
Bell did well to get down at his near post to save a flick from Oliver on 24 minutes then the same Morton player had a rather optimistic shout for a penalty when he bounced off Edjenguele on the half-hour.
A mistake from Edjenguele on 42 minutes caused panic at the back for United but his defensive colleague Mark Durnan did well to sweep up the danger before Tony Andreu blasted over at the other end.
United had been punchless and even jittery in the first period and it was the Greenock men who had to be the happier as they walked off at the interval.
Murray chased down a long ball to win a corner four minutes after the restart but Edjenguele’s header didn’t trouble Gaston.
On 51 minutes, the Tangerines pulled level thanks to a superb goal from Murray.
It was a neat move involving Flood, Andreu and Spittal, who played the ball forward to Murray with his back to goal just outside the Ton box.
Murray spun to his left then unleashed a right-foot shot that flew past Gaston and into the top right-hand corner of the net. It was a cracker and just what the visitors needed.
United had their tails up now and Flood almost squeezed a shot inside the near post, with only a strong hand from Gaston stopping them going ahead.
Wato Kuate was booked as the match approached the hour before Andreu had a shot blocked after being played in by Stewart Murdoch.
The visitors looked the better side now and they took the lead on 62 minutes.
It was another peach, with Kuate doing brilliantly to hold on to the ball before squaring it to Spittal 22 yards from goal.
The midfielder wasted no time in blasting a low shot just inside the left-hand post to leave Gaston stunned as well as the home fans.
Murray picked up a booking before Spittal sent a freekick over the Morton bar on 81 minutes.
The visitors brought on Scott Allardice for Mikkelsen with five minutes left.
Murray fired over at the back post in the final seconds but the work was done and United hung on for a welcome and deserved win that sets them up nicely for Friday.
Greenock Morton: Gaston, Lamie, O’Ware, Oliver, Forbes (Doyle 76), Lindsay, Tidser (Tiffoney 90), Shankland (Oyenuga 81), Russell, McDonagh, A. Murdoch. Subs not used: McGowan, Scullion, Strapp.
Dundee United: Bell, Durnan, Spittal, S. Murdoch, Murray (Coote 90), Edjenguele, Flood, Kuate, Mikkelsen (Allardice 85), Andreu, Robson. Subs not used: Zwick, Dixon, Donaldson, Nicholls, Telfer.
Referee: Willie Collum.