Jim McIntyre’s side could live to regret this opportunity after enjoying the majority of possession and chances against the visitors who were forced to play the last six minutes with 10 men due to substitute Jack Hamilton’s straight red card.
The Dark Blues at least stopped a three-game losing streak to move within two points of second-bottom St Mirren, before facing Tayside rivals St Johnstone on Saturday in their final league fixture of 2018.
Livi, for their part, picked up another valuable point and will not be too disappointed leaving Tayside with just a share of the points.
McIntyre’s first game in charge after replacing Neil McCann ended in a 4-0 thrashing at the hands of Livingston.
That was back in late October and, despite a brief resurgence, they went into this fixture on the back of three straight league defeats.
Livi, on the other hand, were brimming with confidence having recently thumped Hearts 5-0 when all of their goals came in the last twenty minutes.
In their last outing, they had earned a 1-1 draw away to Hibs and were intent on keeping their fine run of form going.
Dundee had left veteran striker Kenny Miller on the bench for last Saturday’s 3-0 defeat at Celtic but the 39-year-old returned to lead the line from the start against Gary Holt’s visitors.
Livingston had outdone the Dark Blues from set-pieces just over two months ago but it was the hosts who threatened from such situations early on, only for some stout Livi defending to keep them at bay.
Then, after 15 minutes, Dundee full-back Nathan Ralph unleashed a left-foot shot from 25 yards which struck Liam Kelly’s crossbar before spinning over.
Calvin Miller then overlapped down the left and crossed for Miller who made contact inside the box but could not keep his effort on target.
The hosts’ next effort came after 32 minutes when Benjamin Kallman turned and shot past the post from a tight angle.
Miller was in the thick of the action for Dundee and, within minutes of the second-half getting under way, he twice brought out saves from Kelly.
Livi’s main threat was from set-pieces although with 10 minutes remaining they did launch a counter-attack, ending in Steven Lawless striking the bar with an ambitious attempt from 25 yards.
Soon after, Dundee midfielder Jesse Curran saw his low left-foot drive trickle just past the post as the hosts kept up the pressure.
With six minutes left, Livi were reduced to 10 men when sub Hamilton was shown a straight red-card for a clash with Darren O’Dea, but the visitors held on.