Former Lions favourite Iain Russell was in the thick of the action after finding the net to cancel out Danny Denholm’s opener for the hosts and earning the penalty for Ryan McGuffie to put the Doonhamers in front.
The spot-kick decision was particularly contentious after Russell’s cross appeared to strike Coll Donaldson’s head and not his arm.
Callum Fordyce headed in a second-half equaliser before Livingston were reduced to ten men when Neil Hastings picked up a second booking.
Substitute Danny Mullen put Livingston back in front with a reaction shot inside the area, but Reilly levelled to notch Queens’ 14th goal from four competitive games.
“We have definitely got goals in us but we didn’t play well today,” said Queens manager Jim McIntyre. “Credit to Livingston, I thought they were better than us.”
Livingston manager Richie Burke said: “We didn’t even have enough players to put on the bench for our full compliment of subs.”