The former Carlisle and Gateshead striker added to his three pre-season goals by scoring twice in three minutes as Motherwell ran amok in the second half.
The visitors got off to the ideal start when Alex Fisher chested Steven Hammel’s cross into the path of Chris Cadden, who finished high into the net from 12 yards.
The Ladbrokes Premiership side were in complete control and Fisher came close with a header, however they came unstuck at a 23rd-minute free-kick. Sean Burns whipped the ball in and Ben Heneghan glanced the ball back towards his own goal under pressure from former Fir Park defender Adam Cummins, who reacted quickest to nod over the line after Trevor Carson had diverted it on to the bar.
Fisher had another couple of half-chances from crosses before the break but Queen’s Park were making it difficult for Motherwell, who started over-hitting balls forward in a bid to break through.
They capitalised on poor defending in the 53rd minute, though, when Burns and Ryan Docherty got in each other’s way. Craig Tanner played a one-two with fellow debutant Gael Bigirimana and slotted home.
Motherwell kept the pressure on and Bowman beat the offside trap to meet Carl McHugh’s lofted pass, round the goalkeeper and slot home in the 74th minute. He then scored a similar second as he ran on to Cedric Kipre’s ball to lob home.
Louis Moult came on to a rapturous welcome and justified the ovation by curling a 25-yard free-kick into the top corner with five minutes left.