Rovers scored all three in the opening seven minutes with Rochina finding the net in the third and fourth minutes and David Goodwillie ramming home the third.
It was the perfect start for Kean's pointless Barclays Premier League side and they held on with ease despite Clinton Morrison's second-half consolation.
Rochina has seen his first-team starts limited since his move from Barcelona last January but he proved his potential with two excellent early goals.
Rochina fired home from a Brett Emerton cross from deep on the right, then within a minute added a second from a tight angle after being fed by Goodwillie.
Goodwillie helped himself three minutes later after a defensive error played in the young Scot down the right and he found the net with a fine right-foot shot.
The League Two side were reeling and another defensive lapse almost let in Rovers again as Danny Batth rammed an attempted clearance against Mauro Formica.
Rochina had a hat-trick effort ruled out for offside and debutant Radosav Petrovic fired over the bar as Kean's men continued to dominate.
Wednesday offered little until first-half injury time when Danny Uchechi headed a Chris Sedgwick cross just wide, but Morrison's half-time arrival helped the visitors.
Gary Megson had made eight changes to the side that had beaten Notts County at the weekend and Morrison immediately galvanised his inexperienced team-mates.
The lively frontman reduced the deficit with his first touch when he was fed by a Chris Lines free-kick and hit a superb left-foot shot across Mark Bunn and into the net.
But Rovers continued to have their chances with Petrovic finding the roof of the net from long-range and Rochina denied a hat-trick once more by a fine block from Reda Johnson.
Petrovic then missed a glorious chance on 65 minutes when he booted over the bar from point-blank range, then O'Donnell got down brilliantly to deny Goodwillie.
Rovers continued to look for a fourth goal and substitute Junior Hoilett fired inches wide shortly after replacing Rochina with 10 minutes to go.
Wednesday might still have made it a nervy final few minutes for the home side but Chris Lines' dangerous late free-kick was deflected into Bunn's arms.