Mikel Arteta's fourth-minute penalty had been cancelled out by Rovers midfielder Steven Nzonzi's 30-yard drive midway through the second half before the introduction of the Nigeria international.
With his first touch seconds after coming on he put his side 2-1 up and although Jason Roberts lashed home an equaliser two minutes later Tim Cahill converted Yakubu's cross from close range late on.
It kept alive Everton's late bid for a European place, moving them to within two points of sixth-placed Liverpool, who play West Ham on Monday.
Aside from the goals Blackburn would argue Arteta should have been sent off after just 20 minutes when he poked Morten Gamst Pedersen in the eye after being angered by the Norwegian's challenge.
Referee Andre Marriner presumably did not see the incident as he booked both players, much to Pedersen's astonishment.
Even by that stage Blackburn had regained the initiative lost by a start which would have infuriated manager Sam Allardyce, whose defence seemed half-asleep when Arteta picked up the ball on the right of the area.
The Spaniard turned Gael Givet and was in the process of doing the same to Ryan Nelsen when the Rovers captain dived in and brought him down with his trailing leg.
Arteta converted from the spot to become the first person to beat Paul Robinson since Birmingham forward James McFadden's goal on March 24, ending an unblemished record of more than five hours.
Rovers' response was encouraging though and they gradually built momentum to the point where Everton were pleased to hear the half-time whistle.
Had David Dunn and Nikola Kalinic not got in each other's way trying to get on the end of Nelsen's header in the six-yard area Tim Cahill's goalline clearance could have been much trickier than it was.
Set-pieces were causing problems for Everton with goalkeeper Tim Howard looking particularly troubled by Rovers' tactic of standing Dunn directly in front of him.
It obviously started to get to him as he gave the midfielder an almighty shove in an attempt to clear some space for one corner but, bizarrely, it was Dunn who earned the talking to from Marriner.
The referee's performance was in danger of overshadowing the game taking place around him as Cahill's late challenge on Dunn warranted only a warning.
In spite of the official, Blackburn carved out a few half-chances, with Martin Olsson's goalbound left-foot volley unluckily blocked by Dunn, who himself was then denied by Phil Jagielka's block.
Just before the break Keith Andrews' drive was saved at the second attempt by Howard, who would have been pleased to find respite in the dressing room.
The interval benefited Everton as they re-asserted their authority and twice could have extended their advantage.
Cahill's last 11 league goals have all been with his head so when Hibbert lofted a 57th-minute cross to the far post and the Australian got in front of his marker it was a major surprise when he failed to hit the target.
Then Leighton Baines' thunderous 25-yard strike cannoned off the outside of Robinson's right-hand post with the goalkeeper motionless.
But where the Everton left-back failed, Steven Nzonzi succeeded in the 68th minute.
There appeared to be little danger when Dunn played the ball back to him but he side-stepped Arteta, advanced and blasted a swerving 30-yard shot past Howard.
The goal was just the confidence boost Rovers needed and Everton looked rattled as Nelsen headed Dunn's free-kick on to the top of the net.
But having tested their opponents all afternoon with set-pieces Blackburn fell victim to one themselves.
Baines' 78th-minute long-throw was flicked on by substitute Victor Anichebe and Yakubu bundled the ball home with his first touch just 22 seconds after his introduction.
Rovers' response was instant as less than two minutes later Kalinic helped the ball forward for Roberts to thrash a 20-yard shot past Howard.
The feeling was there was still another goal left in the game and it went to Everton in the 90th minute.
Yakubu somehow found space on the left of the area and rolled a pass into the six-yard box where Cahill tapped home to deny Blackburn a point.