Skipper Ince sealed only Wolves' fourth win in 16 league games under Hoddle's control when he lashed home a spectacular 30-yard strike on the hour as the draw specialists extended their unbeaten run to ten games.
Burnley's dismal evening was summed up deep into injury time when John McGreal was dismissed for collecting his second yellow card in the space of 17 minutes.
Wolves effectively dominated proceedings for the entire game and the only surprise was that they did not take the lead earlier.
Burnley, who had returned to winning ways against bottom of the table Rotherham last weekend, were made to pay for skipper Frank Sinclair missing the one clear chance that came their way before Wolves broke the deadlock.
Lee Naylor set the tone for Wolves after just seven minutes when his 35-yard free-kick was tipped over the bar by goalkeeper Brian Jensen.
Jody Craddock's shot was blocked by Burnley's on-loan Aston Villa midfielder Peter Whittingham 60 seconds later before Ki-Hyeon Seol stabbed the ball wide after a mistake by Wolves old boy Mo Camara.
Burnley only threatened once in the first period and the miss by Sinclair in the 28th minute was crucial.
The former Chelsea man found himself unmarked when he met Jean Louis Valois' corner but his header bounced over the bar and it was a let-off that
Wolves took full advantage of.
Craddock and Carl Cort again went close to making Wolves' pressure pay before transfer-listed Scottish international Miller pounced seven minutes before half-time.
Ince collected a short free-kick from Mark Kennedy and floated a cross into the area that was headed down by Cort into the path of Miller who stabbed the ball beyond Jensen as Wolves opened the scoring in a game for the first time in nine matches.
That was effectively the beginning of the end of Burnley. Despite an early flurry at the start of the second half when Whittingham and Micah Hyde went close they never really tested Wolves again and Ince ended their comeback hopes in stunning style in the 60th minute.
He ducked under a headed pass from Miller and then raced on to the loose ball before leaving Jensen helpless with a perfectly placed long-range strike to send Burnley crashing to their seventh away defeat of the season.