The former Bolton midfielder was placed in caretaker charge of first team affairs on Saturday following Ian Holloway's decision to take up the vacant position at npower Championship rivals Crystal Palace, and got off to a woeful start with a heavy defeat at Derby.
However, reports that Oyston was locked in talks with an unnamed club - believed to be Portsmouth in a bid to secure Michael Appleton's services - failed to unsettle Thompson as Thomas Ince's eighth goal of the season and Ludovic Sylvestre's late strike inspired the Seasiders to their first win in six outings.
With the Tangerines' fans chanting Thompson's name and the team producing an impressive performance on the pitch, Oyston may now be persuaded to look closer to home for a new boss.
Wednesday - booed off at the final whistle - were second best for much of the game and, although Michail Antonio should have scored, deserved to see their two-match winning run come to an end.
Antonio caused the visiting defence problems early on with his electric pace, but after taking the ball around the onrushing Matt Gilks, his pull back was too heavy for Jay Bothroyd.
Chris O'Grady then headed straight at Gilks before Blackpool settled and Matt Phillips brushed the crossbar with a fierce 25-yard shot.
And Blackpool went ahead in the 18th minute when Phillips released Elliot Grandin down the left and his cutback from the byline was neatly converted by Ince - recently linked with a move to Manchester United - from close range.
Wednesday finished the opening half strongly though with Antonio, aggrieved not to receive a penalty moments before, having a shot beaten away by Gilks and Everton loanee Ross Barkley firing wide.
Antonio had a glorious chance to equalise in the 50th minute. The pacy winger latched on to a long punt up field and created space by cutting back inside before unleashing a wayward effort that flew wide.
The Owls had their tails up and went close again minutes later when Rhys McCabe curled an effort just over from the edge of the box after smart work by half-time substitute Jermaine Johnson.
However, Blackpool showed signs that they were capable of hurting Wednesday on the break when Gary Taylor-Fletcher headed Neal Eardley's sublime cross against the crossbar in the 58th minute.
On-loan Aston Villa striker Nathan Delfouneso was introduced for the tired Taylor-Fletcher and made an immediate impact with eight minutes remaining.
The striker was sent free down the left and after his shot was parried by Chris Kirkland, Sylvestre was on hand to turn the ball into the empty net.