Blackburn scored twice in two minutes to maintain their unbeaten start to the league season away from Ewood Park.
Santa Cruz scored one and set one up for Rovers
A dull first half only sparked into life in the last five minutes when Sunderland striker Michael Chopra had a penalty appeal turned down.
But within 10 minutes of the restart, David Bentley had smashed Rovers in front and Roque Santa Cruz slammed a second into an empty net.
Grant Leadbitter's low 25-yard sidefoot shot was too late to spark a revival.
Rovers boss Mark Hughes kept Robbie Savage and Morten Gamst Pedersen on the bench and gave a start to Santa Cruz who played as a lone striker with Bentley in a free role.
And Paraguayan Santa Cruz was soon in the action, but his header was deflected over the bar by Danny Higginbotham for a corner.
Blackburn enjoyed lengthy spells of possession, but were unable to find the incisive pass, while Sunderland gave possession away far too easily in a disjointed first half.
Liam Miller was handed a start for the home side after scoring the equaliser in last weekend's 2-2 draw at Middlesbrough and he came closest to breaking the deadlock.
He exchanged passes with Ross Wallace on the edge of the box, but Rovers keeper Brad Friedel dealt comfortably with the curling effort.
Chopra was incensed after he went down in the penalty area under a challenge from Friedel moments later, but referee Peter Walton waved away his appeals and awarded a corner.
Rovers' opener came eight minutes after the break when Santa Cruz powered into the Sunderland penalty area. His shot was blocked by Higginbotham but Bentley pounced to volley home.
Provider turned goalscorer 90 seconds later after Brett Emerton raced onto Higginbotham's woefully short backpass.
Emerton's effort was parried by an advancing Gordon, but the Australian had the presence of mind to head across goal to Santa Cruz who finished with aplomb.
Bentley should have killed the game off four minutes later when he danced between two defenders to leave him one-on-one with Gordon, but the Scotland keeper palmed his low shot to safety.
Leadbitter curled a free-kick into Friedel's arms before Black Cats boss Roy Keane introduced three strikers, David Connolly, Daryl Murphy and Roy O'Donovan, but they made little impact as Sunderland continued to waste possession.
Friedel dealt with a couple of tame efforts from Paul McShane before Leadbitter set up an unexpectedly tight finish with a side-footed drive from 25 yards in the 90th minute.
Four minutes of stoppage time followed, but Blackburn's defence held firm to record their second away win of the season.
Sunderland boss Roy Keane
"We gave away two bad goals and we can't afford to do that in the Premier League.
"I was more disappointed with the first goal as we allowed a striker to run 30 yards without a challenge.
"They were soft goals and that is a major disappointment, but credit to the players, they kept going and if we had played another five minutes we may just have got an equaliser - overall I thought we deserved something."
Blackburn boss Mark Hughes
"I wanted my team to dictate the tempo and I felt we did that with the quality of our passing.
"We had good angles to our passing to get good players into good areas in between the lines, and we caused Sunderland a problem.
"They struggled with our movement and it was difficult for them to get a foothold in the game and gain some momentum.
"In the second half, we got two quick goals and from that point, we were very comfortable and never looked like losing the game."
Sunderland: Gordon, McShane, Nosworthy, Higginbotham, Collins, Leadbitter, Yorke (Murphy 66), Miller, Wallace (Connolly 65), Chopra (O'Donovan 66), Jones.
Subs Not Used: Ward, Harte.
Goals: Leadbitter 90.
Blackburn: Friedel, Emerton, Samba, Ooijer, Warnock, Bentley, Kerimoglu (Savage 75), Mokoena, Dunn (Rigters 86), Derbyshire (Pedersen 66), Santa Cruz.
Subs Not Used: Brown, Khizanishvili.
Goals: Bentley 53, Santa Cruz 55.
Ref: Peter Walton (Northamptonshire).