Dundee started slow and got better after 10 minutes with Josh Mulligan and Lee Ashcroft had efforts on goal but were not on target. But Morton took the lead on 17 minutes when the ball was not cleared and O'Connor hooked the ball home.
Dundee had a go to level the game but struggled to create anything of note to trouble the Morton defence, who were happy to waste time when they could. But on 32 minutes Dundee scored when Luke Hannant headed home from a good cross from Zach Robinson.
Josh Mulligan went close with shot but it was just wide of the goal as half time arrived.
Second half and it was much the same vein Dundee did attack but failed to get efforts on target, Morton got the decision of a free kick and it looked the other way but Muirhead scored from 30 yards toput Morton ahead it was a fine finish from the striker.
Five minutes later and it 3-1 when Baird scored with a header it was a poor goal to lose and gave Dundee a hugh mountain to climb.
This time Dundee did respond positively and forcefully. Gary Bowyer threw on Kwame Thomas and Paul McMullan for Alex Jakubiak and Luke McCowan.
Within four minutes Barry Maguire was fouled as he drove into the penalty area from the right. The referee awarded the free kick a foot outside the box despite the crowd’s screams for a spot kick.
It made no difference because Hannant chipped the free kick to the far post where Kwame Thomas headed home.
It gave Dundee hope as they pushed forward to try and get a draw, and four minutes into injury time it arrived when a ball from McMullan was not headed and Kwame Thomas nicked in to smash the ball home to score it could prove a very vital goal and point for Dundee in their bid to win the league.
Next up is a tricky trip up to Inverness CT next Saturday.
Dundee: Legzdins, Mulligan, Ashcroft, Sweeney (c), Marshall, McCowan (McMullan 66), Maguire (Williamson 84), Cameron, Hannant (Reedy 84), Jakubiak (Thomas 66), Robinson. Unused Subs: Lawlor (gk), Kerr, Byrne, Fisher, Clampin.
Referee: Chris Graham
Att: 5,246
