Trialists Paul Taylor and Romario Vieira also found the net along with Alex Kiwomya and Matty Blair while Alfie May bagged a hat trick.
This fixture, against a side from tier nine of the English football pyramid, was originally designated for Rovers' U23s only for new boss Grant McCann to alter the plans as he looked to get minutes into the legs of his senior players.
Such matches involving a significant gulf in class typically occur early in pre-season when fitness and conditioning is more of a leveller.
With Rovers reaching optimum fitness levels as the start of the season rapidly approaches, it should always have been the stroll in the park it proved.
Yet to do so required a good deal of professionalism and composure from McCann's side which, thankfully, they delivered.
McCann reverted to much of the side that faced Birmingham City last week with Coppinger and Taylor the only additions.
Romario Vieira - who came off the bench the previous night against Grimsby Town - was among the substitutes again.
Against Birmingham, this group of players impressed greatly against arguably the Championship side's strongest line-up. It saw them put pressure on what had, rightly or wrongly, been termed Rovers' first choice side.
Doing the same against Deeping was always going to be difficult.
But they should nevertheless be lauded for the professional manner in which they saw out the job.
Rovers settled any nerves with a goal after eight minutes. Kiwomya curled a superb effort in at the far post from the left corner of the box.
May should have doubled the lead when latching onto a long ball from Marko Marosi but put his shot straight at keeper Josh Carpenter.
If anyone was looking for something to ignite the fixture, Coppinger delivered with the second goal on 16 minutes.
Deeping keeper Carpenter sent a long clearance up field which dropped to Coppinger just inside the half. He met the ball with a stunning scythed volley which looped over the keeper and nestled into the roof of the net from a bounce.
Taylor increased the advantage six minutes later with a low drive from just outside the box off a loose ball.
Rovers looked in command but disappointingly dropped their tempo as the half wore on.
And they were caught napping when Dan Schiavi surged clear down the left and cut in a low ball which Billy Stubbs turned in from close range.
Such a drop in levels will not have gone unnoticed and there was no surprise that Rovers returned for the second half with fresh determination.
It took them just three minutes to add to their score when May latched onto a fine ball over the top from Taylor and finished confidently.
Less than a minute later May had his second. Substitute Issam Ben Khemis chipped past a defender and May clipped a low shot beyond Carpenter.
Max Watters looked to have increased the advantage after coming off the bench but his close range finish was flagged offside.
Rovers did not have to wait long for their sixth.
May cut a pass back from the byline after a marauding run and Vieira drilled home a low effort from just inside the box.
Blair put the icing on the cake with a rare headed goal after meeting Danny Amos' fine cross at the far post.
And there was still time for May to complete his hat trick when he surged past the keeper and slotted in from a tight angle.
ROVERS (4-3-3): Marosi, Lund, Wright, Garratt, Amos, Blair, McCullough, Coppinger (Vieira 60), Taylor (Watters 60), May, Kiwomya (Ben Khemis 46). Subs: Jones, Fletcher, Prior, Gibbons, Morris.
Referee: Brian O'Sullivan