They looked set to throw away the win when Steve Howard's 10th goal of the season for Luton cancelled out the first goal of Mark Davies' career.
But Wolves were saved by the never say die attitude of former England skipper Ince who drilled home his shot from 25 yards.
The win, only Wolves' third in their last 10 home league games, moved Glenn Hoddle's side back into the top six.
Luton, who have now lost 10 of their 15 away games this term, badly needed maximum points to kick-start their play-off push. But they failed to reproduce the form that had seen them give Liverpool such a scare in the FA Cup last weekend.
A dire encounter only really came to life when England Youth international Davies gave Wolves a 57th-minute lead.
Davies started and finished the move that led to his goal. He won the ball in midfield and fed Ince who in turn released Mark Kennedy on the left-wing.
Leon Clarke met Kennedy's cross only to see his shot saved by Marlon Beresford. But the rebound fell to Davies who bundled the ball home from close range.
It looked to be good enough to seal victory for Wolves but they failed to build on their advantage, with Kennedy hitting the post, and that gave Luton the chance to force themselves back on to level terms.
They did just that when Howard struck 10 minutes from time. The home defence failed to clear a free-kick from Kevin Nicholls and the Luton skipper was able to float the ball back into the area for Howard to head home from six yards.
Luton looked set to hang on for a point but they underestimated the determination of Ince, who unleashed a fierce drive that took a slight deflection on its way past Beresford.