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Mark Byrne scored the pick of the goals as Gillingham won at home in the league for the first time in three months.
Byrne and Alex Lacey put the Gills incharge at the break and Josh Parker added a third early in the second half.
A sunning volleyed goal from Byrne made it 4-0 but the midfielder missed the chance of a hat-trick after putting another penalty wide.
Liam Sercombe hit a stoppage-time goal for Rovers, finding the top corner with a great finish.
Reaction: A 'mixed performance' for Gills boss Steve Lovell
Gillingham made the one change to their starting XI, with boss Steve Lovell bringing Lacey in to start at left-back ahead of Conor Ogilvie, who wasn’t even on the bench.
Fit-again Bradley Garmston was, however, named among the subs as was striker Conor Wilkinson, back after missing last week’s trip to Plymouth.
Lovell was hoping to celebrate a first home league win since taking charge, the club boasting just one three-point success at Priestfield all season, that coming against Charlton in mid-September.
Gillingham got rid of the home-form issue in some style.
There were several nervy moments early on that they had to deal with, with Rovers testing keeper Tomas Holy twice in the opening seconds, with shots from Rory Gaffney and Ellis Harrison.
Sean Clare and Tom Eaves both went wide for the Gills before Parker tested keeper Adam Smith with a header from a well-worked corner routine.
Rovers were putting the pressure on, however, winning a series of corners, before the Gills finally began to dominate.
Gills right-back Luke O’Neill was instrumental in setting up a couple of goalscoring chances, picking out a run from Parker. Eaves’ touch from the subsequent cross was heavy and that opportunity went.
It wasn’t long before the Gills were ahead. Scott Wagstaff was tripped in the box by Joe Partington – as clear a foul as you will see – and Byrne put the Gills ahead, scoring on the follow-up after his spot-kick was turned onto the post by Smith.
Gillingham dominated the rest of the half and Lacey finished well for the second after playing a one-two with Lee Martin to get in behind.
Eaves should have made it three before the break but Smith made a point-blank save from his header off O’Neill’s cross.
The interval interrupted Gills’ impressive play momentarily and the third goal wasn’t long in coming. Parker chased a deep free-kick from Holy and got a toe-poke on the ball to beat Smith with 48 minutes gone.
It was a goal-of-the-season contender for Gills’ fourth as Martin’s cross was volleyed home by Byrne, with a powerful rising shot that gave Smith no chance.
Byrne could have had a hat-trick on 65 minutes but smashed a penalty wide after keeper Smith had taken the impressive Wagstaff down in the box.
O’Neill went close with a shot just past the post while Harrison put one wide himself at the other end with 10 minutes left.
Wagstaff presented Rovers with a chance to pull one back in the first minute of stoppage-time, with a clearance into his own box. Sercombe made him pay with a great finish into the top corner from the edge of the box.
Gillingham: Holy, O'Neill, Nugent, Ehmer, Lacey (Garmston 75mins), Wagstaff, Byrne, Clare (Hessenthaler 68mins), Martin (Wilkinson 77mins), Eaves, Parker. Subs not used: Nelson, Zakuani, List, Cundle.
Bristol Rovers: Smith, Leadbitter, Brown, Lockyer, Sweeney, Sercombe, Harrison, Bodin, Partington (Broom 77mins), Sinclair (Clarke 62mins), Gaffney (Nichols 66mins). Subs not used: Slocombe, Broadbent, Telford, Bola.
Attendance: 4,227 (309 away)