Dundee made three changes from the team that drew with St Mirren. Ethan Ingram, Josh Mulligan and Seb Palmer-Houlden started in the place of Jordan McGhee, Sam Braybrooke and Curtis Main, who were all on the bench.
Dundee started the game poorly and went behind to a set piece goal after only six minutes, when Wright headed home at the far post. This was after County had missed a good chance two minutes earlier.
It set the tone for much of the first half with Dundee struggling to get going in midfield, too many long balls and which led to the strikers not having much on as chances. The wind did not help matters and hopely they can use it better in the second half.
They were a wee bit unlucky on 30 minutes when Murray turned and shot home, it was ruled off for offside.
The game took a big twist right on half-time, Connor Randall was left alone in space to shoot from 20 yards but he pulled his shot wide. County stayed on the attack and seemed to have won a corner but play was held up for a VAR review and after consulting the monitor the referee decided that Ethan Ingram had pulled Jordan White down off the ball. In the fourth minute of added time White made it 2-0 when he sent Jon McCracken the wrong way from the penalty spot.
Dundee made two changes at half time, sending on Jordan McGhee and Seun Adewumi for Ethan Ingram and Seb Palmer-Houlden.
Dundee were much better in the second half but again failed to turn it into goals. They had a lot of the ball and game ran away from them.
Ziyad Larkeche had a good shot from 25 yards and Dundee made three more changes when Fin Robertson, Curtis Main, and Sammy Braybrooke replaced Ziyad Larkeche, Scott Tiffoney and Josh Mulligan.
Dundee had another couple of half chances but the game ended 2-0 for the home side, who forced McCracken into a good save late on.
First defeat in the league and they must bounce back next week for the Cup game at Ibrox.
Dundee: McCracken, Ingram (McGhee at half time), Portales, Koumetio, Larkeche (Fin Robertson 64)
Mulligan (Braybrooke 64), Sylla, Cameron, Palmer-Houlden (Adewumi at half time), Murray(c), Tiffoney (Main 64). Unused Subs: Carson (gk), Astley, Graham, Vetro.
Referee: Grant Irvine
Att: 4,069