Steve Bruce's men bounced back from their midweek mauling at the hands of Chelsea to record their first home win of the campaign.
But it was far from plain sailing for the home side, who had to come from behind and struggled to cope with Rovers' physical style throughout the encounter.
The Black Cats got off to a very slow start and allowed Rovers to stamp their authority on proceedings early on.
An aerial bombardment forced the hosts on to the back foot as Sam Allardyce's men won a series of corners.
The Wearsiders never really seemed comfortable dealing with the high ball and suffered a number of lucky escapes, mainly due to fouls on keeper Marton Fulop.
But the visitors' pressure paid off on 21 minutes. Morten Gamst Pedersen's corner was flicked on before being cleared off the line by Lee Cattermole, but the ball only reached Gael Givet on the edge of the area and his low drive found the net.
The hosts were still struggling to find any real rhythm, but were back on level terms just after the half-hour mark.
While Rovers persisted with their ugly, but effective up and under routine, the Wearsiders profited from a lovely passing move.
Cattermole won a header just inside his own half finding fellow midfielder Steed Malbranque in the process.
The Frenchman picked out Jones with the deftest of weighted passes and the Trinidad & Tobago international controlled in equally assured measure, before lifting the ball over the onrushing Rovers keeper Paul Robinson and slotting the ball into the empty net.
The home fans may have expected their side to push on after that, but Bruce's side still seemed a little flat going into the half-time break.
Whatever words of wisdom the Sunderland boss had for his side during the break seemed to pay dividends, with the Black Cats appearing far more lively after the restart.
The Wearsiders pressed and harried the visitors, adding an attacking impetus that they had rarely shown in the opening period.
Their fresh approach was rewarded on 54 minutes as they took the lead for the first time in the game.
Sunderland broke down the left with Cattermole crossing from the edge of the area. His centre was met by the head of Jones and while Robinson managed to get a hand to the ball, he was unable to prevent it from finding the net.
Blackburn refused to give up the fight though and continued to pressure the Sunderland rearguard with high balls into the area, winning numerous corners.
And the visitors must have thought they were worth the draw having found the net on 55 minutes only to have their effort ruled out for an offside flag against Chris Samba.
They went close again on 75 minutes when substitute Benni McCarthy headed against the bar and Sunderland somehow managed to scramble the ball clear.
But the ball just wouldn't run for Rovers, a fact which was highlighted in the dying seconds of the game.
With the clash having gone into four minutes of added time Croatian Nikola Kalinic fired wide when it seemed easier to hit the target.
It was a gilt-edged chance which had gone begging and had taken with it any hope that Rovers had of getting something from the game.
The Black Cats defence may have used up one of their nine lives, but that won't worry Bruce, who will just be glad of the three valuable Premier League points.