Potter's first goal since August was the second perfectly-executed finish, hardly in keeping with a drab encounter that was otherwise short on quality.
But most in a crowd of 19,058 will care little about how Wednesday keep chalking up the wins.
This was their fifth in seven league matches since Alan Irvine arrived at the club early last month with the remit of ensuring Championship football next season.
Blackpool's season is beginning to unravel. The Seasiders, just two points adrift of the play-offs going into the match, have slumped to three successive defeats and have won only one of their last eight in the league.
The Owls were unchanged from the side that made a fist of it on Saturday before being edged out at Nottingham Forest, but Blackpool manager Ian Holloway made sweeping changes.
Barry Bannan, Neal Eardley and Ishmel Demontagnac were all dropped for partying in a Blackpool nightclub on Saturday night, while goalkeeper Paul Rachubka, Jason Euell, Rob Edwards, Andy Butler and DJ Campbell all returned to the side.
Wednesday made a flying start thanks to full-back Tommy Spurr's storming run and cross down the left wing.
Spurr picked out the unmarked O'Connor eight yards from goal and the Owls midfielder rose to plant a firm header into the top corner in the second minute.
Michael Gray blazed Varney's lay-off over the crossbar and at the other end Euell flashed his effort off target, but after half-an-hour neither goalkeeper had been troubled.
The visitors then burst into life momentarily, breaking swiftly with Campbell heading Stephen Dobbie's right-wing cross just wide.
Wednesday almost scored within two minutes of the restart when Potter's deflected shot from the edge of the penalty area forced Rachubka into a smart save.
But Potter left the visiting goalkeeper flailing at thin air in the 50th minute.
The Owls midfielder controlled Varney's short pass 18 yards out and deftly turned inside his marker before curling a low left-footed shot inside Rachubka's right-hand post.
Wednesday central defender Darren Purse displayed his growing stature with a superb-timed tackle to deny Campbell in the area.
Rachubka saved well to deny the home side a third goal in the 67th minute after Tom Soares had picked out Varney 10 yards from goal.
Blackpool stepped it up in the last quarter but lacked the urgency in front of goal to catch a solid Wednesday rearguard flat-footed.