David Dunn got the ball rolling in the fifth minute and Hoilett's goal gave Rovers breathing space.
It was breathing space they needed as Simeon Jackson pulled one back from the penalty spot 21 minutes from time, but Morten Gamst Pedersen's corner went in via an unfortunate deflection from Gills skipper Barry Fuller five minutes later to seal the win.
Rovers made seven changes from the side beaten at Sunderland on Saturday and after a blistering start it was one of the new faces who put them in front.
Nicola Kalinic was the architect, getting free of John Nutter and laying the ball in to Dunn who slid the ball home under Simon Royce.
That was about as good as it got for the Croatian though as he endured a frustrating full debut in the Rovers attack.
The £6million signing from Hajduk Split had missed a host of chances after his introduction as a substitute at the Stadium of Light on Saturday, but had even less joy at Priestfield with makeshift centre-back Mark Bentley keeping him out of the game, while he was also booked for diving before being replaced by Jason Roberts at half-time.
Royce had already been called in to action to tip over Pedersen's free-kick before Dunn's goal, but the Gills gave a good account of themselves for the rest of the half.
Mark McCammon, making his first start of the season in the Gills attack, was a lively presence and came closest to a leveller for the Kent club when he met Jackson's cross at the far post but headed across the goal and just past the post.
Hoilett shot just wide for the visitors before former Gills stopper Jason Brown did well to keep out Fuller's free-kick, and McCammon was unable to score from the rebound.
Steven Reid was forced off at half-time as Vince Grella also joined the fray, and Rovers were two up within a minute of the start of the second half when the impressive Hoilett gave Royce no chance with a diving header after Keith Andrews' cross was deflected to him.
Rovers were rampant and Steven N'Zonzi headed just over the top, before Hoilett was also narrowly off target after good work from Roberts down the left.
Jackson had his first sight of goal from Fuller's cross-cum-shot but Brown clung on with little fuss, before Royce kept his side in it with a stunning save from Roberts' header.
And the Gills then went straight up the other end and got themselves right back in it when Jackson tumbled in the box under a challenge from Zurab Khizanishvili and the Gills top scorer picked himself up to score the penalty in the 69th minute.
But five minutes later the game was all but over when Pedersen's vicious inswinging corner was too good for the Gills defence and went in, despite the best efforts of Fuller on the line.
Rovers saw out the clash comfortably to progress to the third round and leave the Gills on the end of a fourth successive defeat - but they will be able to take heart from their battling efforts.