Rovers continue to look nervously over their shoulder after a disappointing 2-0 defeat at Everton.
Steve Kean's side sit just two points above the drop-zone after a below par performance at Goodison Park.
Both teams were off colour in a first half that offered little, but it was the home side that drew first blood early in the second, Leon Osman seeing his shot on the angle diverted home by Christopher Samba.
Any chance of a come back ended when Leighton Baines drove home a 74th minute penalty after Phil Jones had upended Seamus Coleman in the area.
Morten Gamst Pedersen should have reduced Everton's advantage with thirteen minutes to go but he volleyed wide from eight yards out summing up a disappointing afternoon for Rovers.
Steve Kean made three changes from the side that drew with Birmingham City seven days earlier. Two were enforced as Ryan Nelsen and Junior Hoilett missed out through injury, whilst Morten Gamst Pedersen dropped to the bench.
After impressing for the Reserves on Monday night in which he bagged a brace, Ruben Rochina was given his first Premier League start. Gael Givet returned to the defence, with Brett Emerton preferred to Morten Gamst Pedersen in midfield.
The match was slow to get going, Jermaine Beckford's early effort a rare chance in a first half where neither goalkeeper was tested.
Ruben Rochina showed some neat touches on his first start, operating in a floating role behind Roque Santa Cruz.
The home side had more of the ball, but rarely carried a threat. Phil Neville and Leon Osman failing to test Paul Robinson, whilst at the other end a ball sent for Santa Cruz just wouldn't drop in time for the Paraguayan to take advantage of.
The half time whistle was met with a muted reaction from the home support, Rochina's display a rare spark in an otherwise ineffective first 45.
Thankfully the opening ten minutes of the second half had more chances than the entire first period. But from a Rovers point of view the ones that counted didn't come their way.
David Dunn did fashion the first effort after the break, cutting in from the left to curl a shot that just evaded Tim Howard's far post on 49 minutes, but three chances in the space of a similar number of minutes would see Everton eventually break the deadlock.
Magaye Gueye fizzed a shot just past Paul Robinson's right post, then Leighton Baines was equally close at the other side with a low strike from 20 yards after the ball broke to him from a corner kick.
It was from a 53rd minute corner kick that the home side scored. Gueye's short corner to Leon Osman saw the midfielder run unopposed into the area to shoot across goal, his strike taking a decisive touch off the outstretched boot of Chris Samba to divert it into the back of the net.
Rovers looked for a way back, Jason Roberts and Morten Gamst Pedersen were brought on for Roque Santa Cruz and Gael Givet, but from a quick-fire Everton break they were handed a second goal.
Rovers had been on the attack, but with numbers still forward the home side raced upfield, Phil Jones diving in on substitute Seamus Coleman to bring him down for a clear penalty.
Leighton Baines took the spot-kick duties, making no mistake from 12 yards, lashing the ball high to Robinson's left.
Rovers should have reduced the deficit on 77 minutes, a Brett Emerton cross caused confusion between Baines and Jagielka as they both went for the ball, to dropped to Morten Gamst Pedersen but he drove wide on the half volley from ten yards.
Benjani was brought on for the final ten minutes, replacing the tiring Ruben Rochina who had looked bright on his first start, but the Zimbabwean had little affect as Everton saw out the remaining minutes with relative ease.
EVERTON: Howard, Hibbert, Baines, Heitinga (sub Rodwell 15 mins), Jagielka, Bilyaletdinov, Distin, Beckford (sub Vellios 85 mins), Neville (c), Gueye (sub Coleman 65 mins), Osman.
Subs not used: Mucha (GK), Anichebe, Mustafi, Forshaw.
ROVERS: Robinson, Salgado, P. Jones, Samba (c), Givet (sub Pedersen 68 mins), Emerton, Dunn, J. Jones, Olsson, Rochina (sub Benjani 81 mins), Santa Cruz (sub Roberts 61 mins).
Subs not used: Bunn (GK), Kalinic, Hanley, Diouf.
Booked: Baines (Everton), Dunn, Rochina, P. Jones (Rovers).