David Goodwillie earned Blackburn a precious point with a 1-1 draw at Goodison Park after Tim Cahill had ended a 13-month goal drought to put Everton ahead.
The Australian, who had not scored since a clash with Manchester City on December 20, 2010, took advantage of some poor defending to tap home in the 24th minute.
Blackburn had hit the woodwork twice in the first half but it took them until 18 minutes from time to level when Goodwillie bundled in in an attempted clearance from Cahill, and they rode their luck to hang on for a draw.
Everton had picked up only four points from their previous four home matches but they probably should have been ahead inside three minutes when a Landon Donovan cross found Anichebe eight yards out but he scuffed his shot on the turn and it bounced wide. Rovers also looked bright going forward and David Dunn was denied twice in quick succession.
Tim Howard pushed a corner over his bar but needed help from the second set-piece, Leighton Baines doing brilliantly to keep out a Scott Dann header with help from the woodwork. Blackburn were enjoying much of the possession but went behind as Cahill finally ended his goal drought on 24 minutes, although in controversial circumstances.
Dunn's decision to stay on the line after a corner had been partially cleared proved costly for Rovers as Donovan's chip back in found Marouane Fellaini in acres of space eight yards out. Paul Robinson blocked his initial effort and when the ball came back out to the Belgian he appeared to control it with his hand as he found Cahill for a simple finish.
Everton almost had a second nine minutes later but Donovan could not keep his shot down after he had been well found by Cahill. Rovers had another chance when Goodwillie's deflected shot fell to the impressive Dunn and his curling effort beat Howard but bounced back off the post.
After Fellaini had seen his shot hit team-mate Louis Saha, Robinson gratefully snaffled Cahill's header when it looked to be creeping inside the post. Blackburn finally equalised in the 72nd minute with a goal not unlike the one they conceded earlier.
Howard missed a lofted ball from Pedersen under pressure from Steven Nzonzi which bounced off Shane Duffy's head to Cahill on the line, and his clearance hit Goodwillie in the midriff and bounced into the net.
A crazy goalmouth scramble looked certain to bring an injury-time winner for the Toffees after Robinson had pushed a Fellaini effort behind. Donovan's corner picked out the Belgian and, after his header had been cleared off the line by Mauro Formica, Robinson saved a shot from Denis Stracqualursi and Cahill's effort was blocked as Rovers somehow held on.