Brave Blackburn twice came back from behind to equalise through spectacular goals from Steven Nzonzi and Jason Roberts, but Cahill sealed the victory as he joined Mikel Areta and substitute Yakubu on the Everton scoresheet.
Rovers, looking for their fourth successive clean sheet, made three changes from the side which held Manchester United to a 1-1 draw six days earlier. Keith Andrews, Ryan Nelsen and David Dunn returned at the expense of Brett Emerton, Chris Samba, both injured and Vince Grella.
Everton, unbeaten in their last seven, home and away, welcomed back Arteta and Tony Hibbert, while Louis Saha was preferred to Yakubu in attack.
The visitors got off to the ideal start when Arteta fired them in front from the penalty spot after just four minutes after a foul by Nelsen on Cahill.
Cahill had to be alert to keep out a good chance for Rovers on 14 minutes as he cleared a shot from Dunn off the line after Tim Howard had parried a header from Nelsen following a corner.
On 20 minutes, a spat between Arteta and Morten Gamst Pedersen which threatened to boil over resulted in both players being booked.
Rovers' threat on goal increased as the half went on and shortly after Martin Olsson had had a shot blocked in a crowded goalmouth, Pedersen just failed to get a touch on a loose ball after Nikola Kalinic had had a shot on the turn saved by Howard.
A minute before the break, the ball fell ideally to Andrews on the edge of the Everton penalty area but his shot was straight at Howard, who saved easily.
Everton remained firmly in control in the opening minutes of the second half and in a bid to press for the equaliser, manager Sam Allardyce sent on Jason Roberts and opted for two in attack as he lined up alongside Kalinic.
Everton's Leighton Baines had a 25-yard shot cannon back off the woodwork a few minutes later, but Rovers didn't have to wait long for their leveller, as on 73 minutes Nzonzi lashed the ball past Howard from 30 yards for his first goal at Ewood.
But with 11 minutes to go, Everton were ahead again when, second after coming on as a substitute, Yakubu touched the ball in from close range after a long throw from Baines had been headed on by Victor Anichebe.
The visitors' joy was short-lived, however, as Rovers had a super sub of their own to thank for their second equaliser of the afternoon.
Roberts ran on to a pass through from Kalinic and drove the ball low firmly past Howard into the bottom left hand corner.
But in the final minute of normal time, Everton took the lead for the third time as Yakubu surged past Phil Jones and crossed for Cahill to turn the ball in from point-blank range.