David Goodwillie earned Blackburn a precious point 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.
Blackburn boss Steve Kean chose to leave out captain Christopher Samba completely after he submitted a transfer request this week while top scorer Ayegbeni Yakubu was suspended and new loan signing Anthony Modeste only on the bench.
The Samba situation has cast a black cloud over what should have been a positive week for Rovers following their 3-1 win over Fulham last weekend, achieved with 10 men, which lifted them out of the bottom three.
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 a spell of intense pressure began when David Dunn was denied twice in quick succession, first by Tim Howard and then a Johnny Heitinga block.
Howard pushed the resulting corner over his bar but needed help from the second set-piece, Leighton Baines doing brilliantly to keep out a Scott Dann header with a bit of help from the woodwork.
Blackburn were enjoying much of the possession but in the 24th minute they went behind as Cahill finally ended his goal drought, although in controversial circumstances.
Dunn's decision to stay on the line after a corner had only 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.
The relief around Goodison Park was audible and 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 have had plenty of reasons to bemoan their luck this season and they had another moment today when Goodwillie's deflected shot fell to the impressive Dunn and his curling effort beat Howard but bounced back off the post.
Both defences looked shaky and, 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 had deserved something and they 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.
Suddenly Rovers looked a real threat and Hoilett saw a shot deflected behind before Kean sent on new man Modeste, who has been disappointing for Bordeaux this season, in place of the goalscorer.
Everton came mighty close themselves, though, Duffy's superb header slamming against the bar from an inswinging Baines free-kick, while at the other end Mauro Formica shot just wide.
And 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 big midfielder and, after his header had been cleared off the line by Formica, Robinson saved a shot from substitute Denis Stracqualursi and Cahill's effort was blocked as Rovers somehow held on.