A Nacho Novo double was enough for Dundee to take all three points against Livingston.
Lee Makel's 30-yard shot was well off target as the visitors tried to get into the game with ten minutes played.
With 17 minutes played Dundee took the lead with a spectacular goal from Novo. A long ball over the top of the Livingston defence by Garry Brady was met on the volley by Novo who from ten yards sent a cracking right foot shot past Alan Main.
Another long-range effort by the visitors went high over the crossbar with half an hour gone. This time Brian Kerr was the culprit. Ten minutes before half time Barry Wilson headed Makel's cross well wide of the target.
With 37 minutes played the visitors drew level when Barry Wilson found space down the right and his near-post cross was flicked past Julian Speroni off the left foot of Burton O'Brien.
Steve Lovell had a half chance for the home team ten minutes after the break but Alan Main did well to save at the Englishman's feet.
Dave Mackay had the home team's next chance and should have at least hit the target from Brady's corner, but the home defender headed wide.
With eight minutes remaining it looked like the visitors would take the lead but the home defence somehow managed to scramble the ball clear when it looked like Fernando Pasquinelli was going to score from close range.
A minute later Dundee were awarded a penalty when Oscar Rubio fouled Fabian Caballero inside the box.
Alan Main dived to his left and got his hand to Novo's spot kick but could not keep the ball out and Novo claimed his second of the game and secured the points for the home team.