Jim McIntyre’s side were striving for some welcome respite from their strained fight against relegation from the Premiership, which has seen luck desert them on countless occasions.
But instead they struggled to scrape a draw and had Jesse Curran, their Australian midfielder, to thank for his equaliser on the stroke of half-time which cancelled out Stephen Dobbie’s 28th-minute opener for Gary Naysmith’s Championship visitors.
Dundee must now travel to Palmerston for a fourth-round replay on 29 January after their manager confessed they could easily have tumbled out.
“I thought Queen of the South were better than us,” admitted McIntyre. “So I’m just glad we’re still in the cup and have another chance to rectify that performance.”
There were debuts for Seny Dieng, the new Dundee keeper, as well as Craig Curran who joined earlier in the transfer window from neighbours Dundee United.
Andrew Nelson had to be content with a place on the bench after the21-year-old striker signed from Sunderland during the week, while the same applied to on-loan Scunthorpe United winger Andy Dales following his move north of the border.
Queens took a deserved lead. A simple move set Josh Todd galloping down the left and his first instinct was to square for Dobbie who did the rest. The 36-year-old kept calm to pass the ball into the net beyond Dieng for his 33rd goal of the season.
A few minutes later, Dobbie turned creator by lashing a ball across the face of the goal in the hope of finding team-mate Lyndon Dykes, but this time he was foiled by Dundee defender Ryan Inniss.
Despite their struggle, the home team levelled at just the right time as Curran shuffled the ball to his favoured right foot before beating visiting keeper Alan Martin courtesy of a rasping 20-yard effort.
Dales replaced Roarie Deacon, who’d been largely ineffective for the majority of the first-half, and he lacked no appetite in trying to impress on his debut.
Dobbie, at the other end, carried menace every time he gathered possession although his 57th minute shot lacked the necessary conviction to trouble Dieng.
Soon after, though, Queens ought to have restored their advantage. Dobbie released Todd whose initial effort from 10-yards was blocked by Dieng, before the Queens attacker’s shot from the rebound was deflected over by Cammy Kerr.
“I’m very proud of how we played and just a little disappointed not to have made it through at the first attempt,” reflected Naysmith afterwards.