Rovers were the first to threaten in a quiet start to the game when Tom Cairney raided down the left and lifted a cross into the area for James Lowe, but his effort was deflected just wide of the post.
Brighton took the lead in the 35th minute when they were awarded a penalty as Dickson Etuhu brought down Conway in the area and Barnes made no mistake from the spot in firing past Kean.
Jake Forster-Caskey came close to doubling the home side's lead after the break when his free kick from just outside the penalty area went inches wide of the post with Kean scrambling to get across to the ball.
Minutes later Forster-Caskey did get Brighton's second goal when he made a late surge into the box and headed Conway's pinpoint cross from the left past Kean into bottom corner.
The visitors almost got back into the game when Tommy Spurr headed an effort off the bar from a corner which was then cleared into the path of Cairney, who blasted a shot at goal but Tomas Kuszczak was there to make a good save.
However, the hosts made sure of the points when Barnes got his second goal of the game when he tapped home from close range after Kean could only parry Andrew Crofts's effort right to him inside the box.