Swansea dominated and went in 2-0 ahead at half-time after a stunning effort from Gylfi Sigurdsson (pictured) and a goal from Nathan Dyer.
A Scott Dann own goal completed a miserable day for Blackburn who remain second from bottom in the Premier League.
Left-back Neil Taylor and winger Wayne Routledge were taken off at half-time during Swansea's poor 3-0 loss at Queens Park Rangers; Taylor survived to start against Blackburn but Routledge's replacement, the returning Dyer, got the nod.
Blackburn wide-man Martin Olsson was only fit enough for the bench because of a groin injury but his twin brother Marcus started the game. Bradley Orr also recovered from an Achilles injury to start.
After a positive start from the visitors, Swansea settled and started to dominate possession.
Sigurdsson felt he was fouled from behind by Morten Gamst Pedersen in the penalty area, but saw his appeals waved away.
The first meaningful save of the match preceded the opening goal 10 minutes before the break. Sigurdsson let fly with a vicious long-range effort that swerved before being beaten away by Robinson.
But there was nothing the former Tottenham Hotspur goalkeeper could do to keep out the Icelander's shot moments later as Sigurdsson received a pass from Joe Allen on the right of the penalty area. He controlled with his right foot and curled a sumptuous effort over Robinson with his left. It was a stunning strike from Sigurdsson and his first at the Liberty stadium since joining the club on loan from Hoffenheim in January.
Swansea soon doubled their lead after a poor piece of defending from Dann. In trying to clear, the former Birmingham City defender gifted the ball to Scott Sinclair in the area. Sinclair passed to Danny Graham, who found Dyer at the back post and the winger fired home with the outside of his right foot.
The Swans continued to dominate in the second-half, with Anthony Modeste and David Goodwillie's introductions at the expense of the subdued David Hoilett and Yakubu doing little to change the pattern of the game.
The home side made the game safe in the 63rd minute. Sinclair produced an excellent run to take him past Goodwillie, Jason Lowe and Bradley Orr before crossing to Sigurdsson who hit the post. The ball came back out and was knocked over the line by Dann for his second own goal of the season.
David Dunn immediately headed a presentable chance over at the other end before striking the post with a long-range effort that had Michel Vorm beaten all ends up.
Swansea continued to dominate against a Blackburn side who seemed content to soak up pressure without offering any kind of punch at the other end.
Sinclair played a neat exchange with Graham before forcing a low diving save out of Robinson as Swansea threatened to run riot.
Substitute Leroy Lita controlled on the edge of the area, turned, and forced another smart low save out of Robinson as Swansea failed to add a fourth but brought an end to a four-match losing run and left Blackburn still three points adrift of safety in the penultimate spot in the table.