A point was the least Rovers deserved after they came from behind to draw at Goodison Park.
Rovers dominated the first half, seeing a Scott Dann header cleared off the line and a David Dunn strike hitting the post, but ended up trailing at the break thanks to Tim Cahill's strike after Marouane Fellaini handled.
The second half followed a similar pattern, but Rovers weren't to be denied, David Goodwillie bundling home from inside the six-yard box after Everton failed to deal with Morten Gamst Pedersen's free-kick.
Mauro Formica could have won it for Rovers when he fired narrowly wide, but then arguably saved his side when he cleared off the line deep in injury time.
Rovers made two changes from the side that played so well in the 3-1 win over Fulham seven days earlier. Scott Dann, back from injury, was returned to the starting eleven, replacing Grant Hanley who unfortunate to drop to the bench.
The other change saw David Goodwillie start his first Premier League game since October, replacing the suspended Yakubu following his red card last weekend.
New loan signing Anthony Modeste received his international clearance in time and was named amongst the substitutes.
Boosted by last week's victory, Rovers were quick out of the traps with a scintillating spell of football. The first twenty minutes saw the home side no match a resurgent Rovers, the only thing lacking in their play was a deserved goal.
After just seven minutes Rovers were thwarted by a smart save from Tim Howard, great skill by Junior Hoilett saw him skip past Fellaini and Neville before feeding David Dunn, he turned and shot but Howard saved with an outstretched boot.
Then Morten Gamst Pedersen played in the lively Dunn but John Heitinga was quick to block the shot for a corner.
Pedersen's first bite from the kick was to see his inswinger tipped over by the back-pedalling American, his second found Scott Dann at the back, the returning defender headed towards the corner of the goal only to be denied by a combination of Phil Neville and Leighton Baines who cleared from their own line.
Dunn was proving to be a real thorn in the Everton side, finding space at will and attacking the Toffee's back line. On 12 he tested Howard with a smart shot after checking inside, a minute later he found the back of the net with a superb turn and volley but unfortunately the flag was up for offside.
The home side had offered very little going forward but somehow on 24 minutes they were celebrating being in front.
Awarded a corner that perhaps shouldn't have been, but they took full advantage, and as Rovers failed to cleared their lines, Landon Donovan's centre found Marouane Fellaini in the six yard box and he handed the ball off to Tim Cahill to score from close-range.
The Rovers players to a man screamed for hand ball by the big Belgian, but an unsighted Mark Halsey allowed the goal to stand.
Despite the injustice of the opening goal Rovers didn't let their heads drop, coming within a lick of paint from levelling on 37 minutes.
Again it was Junior Hoilett causing issues, he found Goodwillie who saw his effort deflected as far as Dunn, but as he steered the ball goalwards it bounced off the foot of the post and away to safety.
The resumption of proceedings after the break saw Rovers continue to dominate the game. With Radosav Petrovic and Steven Nzonzi driving from midfield and Hoilett and Dunn causing issues further forward it was only a matter of time before they levelled.
Petrovic went close with a shot across the bows, the Serbian's sweet strike from the corner of the area flashed just a yard wide of goal, you could sense the goal was coming.
And arrive it did when on 72 minutes Rovers finally got the leveller their play deserved. Morten Gamst Pedersen sent a free kick into the penalty area, Steven Nzonzi made enough of a nuisance to Tim Howard to see the ball bounce off Shane Duffy back towards his own goal. Tim Cahill blocked the ball on the line, but with David Goodwillie closing down the Australian could only clear against the Scotsman and the ball bounced over the line.
Anthony Modeste came on soon after for his Rovers debut, replacing goalscorer Goodwillie, but it was at the other end where the action was centred.
After being on the back foot for so long, it was somewhat against the run of play that Everton struck the crossbar. Leighton Baines' brilliant free kick headed against the bar by Shane Duffy.
Rovers responded with a chance of their own, Steven Nzonzi spotting Jason Lowe on the overlap, his centre was left by Anthony Modeste for Mauro Formica but as he shot beat Tim Howard it fell just the wrong side of the upright.
For those of a nervous disposition the four added minutes at the end of the game couldn't have been worse.
Just on ninety minutes Paul Robinson pulled off a brilliant save to thwart Fellaini, then from the resulting corner kick, Fellaini saw his effort cleared off the line by Formica, Robinson denied Stracqualursi on the follow-up and Petrovic hacked away, it was heart in the mouth stuff.
Thankfully there were to be no further scares as Rovers saw out the rest of the added minutes without incident, the boos ringing out from the home fans at the final whistle telling its own tale.
It was a well earned point from the hard working Rovers, but in truth it should have been more.
EVERTON: Howard, Baines, Gibson (sub Stracqualursi 87 mins), Heitinga, Saha (sub Drenthe 55 mins), Donovan, Cahill, Neville (c), Fellaini, Anichebe (sub Vellios 80 mins), Duffy.
Subs not used: Mucha (GK), Hibbert, Bilyaletdinov, Gueye.
ROVERS: Robinson (c), Lowe, Dann, Givet, Olsson, Pedersen, Nzonzi, Petrovic, Hoilett, Dunn (sub Formica 60 mins), Goodwillie (sub Modeste 76 mins).
Subs not used: Bunn (GK), Rochina, Vukcevic, Hanley, Henley.
Booked: Gibson, Drenthe (Everton), Petrovic, Hoilett (Rovers).