Wolves lost Joao Gomes to a controversial red card within the opening nine minutes and eventually went 1-0 down just before half-time when Neal Maupay swept home.
But the visitors rallied and a Doyle screamer from 25 yards made it 1-1 in style.
Both sides had chances to win it in the remaining minutes but had to settle for a draw and the teams will now return to Molineux with a FA Cup fourth round spot up for grabs.