The visitors led 1-0 at the break thanks to Corry Evans’ magnificent early strike into the top corner.
But McClean, who was perhaps fortunate to escape a red card for a lunge on Markus Olsson seconds before the interval, restored parity just after the hour mark with a bullet header from Shaun Maloney’s free-kick.
Rovers had chances to win it in the final quarter, but Jordan Rhodes’ volley was headed off the line by Leon Barnett, while Jason Lowe saw a late header cleared off the line by Maloney.
The home side started the brighter and could have been ahead with their opening attack.
Adam Forshaw’s powerful shot was superbly blocked by a visiting defender, with the rebound falling back to the midfielder.
This time he went for a more lofted approach and saw his effort narrowly clear the crossbar.
Blackburn held firm at the back from subsequent attacks and it was the visitors who took the lead with their first real attempt on goal.
A Craig Conway corner was half-cleared to Tom Cairney, who teed up Evans on the edge of the area.
The connection was perfect and the ball arrowed into the top corner, with Scott Carson left clutching at thin air.
Rovers saw another shot deflected inches over as Wigan struggled to clear their lines, with Rhodes then heading wide from a good position.
McClean was looking typically busy up front for Wigan and his cross nearly found Martyn Waghorn before the Irishman saw another shot blocked by a defender.
Blackburn had a great chance to increase their lead just before the break when Rhodes was played clean through on goal.
However, Carson stood strong and made a very good stop to his right.
There was then a flashpoint right on half-time as McClean slid in to block a clearance from Olsson and appeared to catch the Rovers man with his follow-through.
The Rovers players were incensed, with plenty making their feelings known to referee Mike Jones, who opted to brandish only yellow.
Blackburn started the second period in the ascendancy and Rhodes had a shot blocked before Matthew Kilgallon saw his effort saved.
Emyr Huws joined Maloney off the bench for Wigan and the latter was involved in the equaliser just after the hour mark.
Kilgallon fouled Waghorn in the air as they competed for a long ball and Maloney’s subsequent delivery into the area was inviting.
McClean rose highest and he planted his header into the roof of the net to the delight of the home supporters.
As the game entered the final quarter it was end-to-end stuff, with both sides trying to edge a keenly-contested encounter.
Rovers wasted a golden opportunity to win it when substitute Josh King raced through the middle and rounded Carson, only to see the goalkeeper recover to parry his shot.
The ball rebounded to Rhodes, eight yards from goal and with a virtual open goal to aim at.
However, the volley was somehow headed off the line by Barnett and away to safety.
Rovers had another chance in the closing stages, but Jason Lowe’s header was hacked off the line by Maloney.
Substitute Andy Delort had a couple of late shots saved by Jason Steele.