The Welsh side had seen themselves concede 10 goals and score just one in that quartet of defeats but bounced back by netting three of their own to deny Rovers a clear path out of the drop zone.
Gylfi Sigurdsson, who had tested Paul Robinson with a dangerous long range effort in the 36th minute, put his side ahead moments later when he received a ball from Joe Allen on the right side of the area before taking a touch, setting himself, and then curling in a lovely left-footer for his seventh since joining on loan from Hoffenheim in the winter.
Six minutes later and Swansea were two to the good when Nathan Dyer netted his first in ten when Danny Graham played him in and he finished with a first-time sliced effort from just outside the six-yard box.
The contest was wrapped just after the hour-mark when Scott Dann unfortunately turned Scott Sinclair's byline cutback into his own net after it had bounced back off the post from Sigurdsson's attempt.
David Dunn hit the woodwork a few minutes later but the damage had already been done as Blackburn's hopes of survival took a turn as they continue to sit three points from safety with four games remaining.
Liberty Stadium, Swansea
Yellow cards:SWA - nil BLA - Junior Hoilett 33', Mauro Formica 90+1'