All the goals came in the second half as Leon Best, a brace from Ruben Rochina, and a Jack O'Connell header saw Gary Bowyer's side claim victory.
22 players played for Rovers as the manager named a different 11 for each half, with all getting a useful 45 minutes under their belts.
It was the Conference side who started the brighter of the two sides in the first half, Rovers struggling to get to grips with the unfamiliar surroundings at the New Bucks Stadium.
After four minutes only an excellent tackle by Anthony O'Connor prevented the home side from getting in on goal, Andy Owens denied by a last-ditch intervention by the Irishman playing at left back.
An unwelcome delay followed at the midway point of the half after the near-side linsman collapsed. Thankfully reports are that he just succumbed to the humid conditions.
After that untimely break it was Rovers who ended the first half the stronger of the two sides, An excellent tackle from Neil Byrne denied Jordan Rhodes as he looked the break through. Whilst Tom Cairney volleyed just wide and Josh King was also off target with a snatched effort.
On the stroke of half time a mistake from right back Ben Marshall saw Sean Clancy get a clear site of goal, but whilst Simon Eastwood couldn't hold the shot, Rovers were able to clear the ball away.
Rovers changed their entire eleven for the second half, as did the home side with the exception of their goalkeeper Jonathan Hedge.
Only a fantastic double save from Jake Kean prevented Telford taking the lead moments after the restart, the Rovers stopper denying Josh Hancock and Andy Todd in quick succession.
Rovers raced up the other end with Devarn Green, playing for the seniors for the first time, saw his goalbound shot deflect over the bar. After that it was Gary Bowyer's side who really stepped it up with the hosts having no answer.
The opening goal came on 56 minutes, the lively John O'Sullivan worked his way towards goal before feeding Leon Best and the striker made no mistake with a vicious effort from outside the area into the corner of the net.
On the hour the lead was doubled with Best turning provider on this occasion, chasing a Lee Williamson ball over the top he squared it for Ruben Rochina who made no mistake from 12-yards with a first-time strike.
It could have been three moments later as the impressive Devarn Green played a lovely one-two with Williamson only to be denied by the goalkeepers legs.
With 15 minutes to go Ruben Rochina grabbed his second of the game, capitalising on some hesitant defending to flick the ball into the roof of the net in fine style after a neat pass from Best.
As the home side struggled to gain traction further forward it was Rovers who added fourth and final goal two minutes from time. A ball into the box from Adam Henley was nodded back across the area by Luke Varney to where defender Jack O'Connor arrived to steer his header beyond Hedge and into the net.
AFC Telford 1st half: Hedge, Baynes, Owens, Byrne, McDonald, Barnett, Cooke, Goddard, Smith, Deacy, Clancy.
AFC Telford 2nd half: Hedge, Booth, Lever, Platt, Akrigg, Grogan, Todd, Ainscough, Farrell, Gray, Hancock.
Rovers 1st half: Eastwood, Marshall, O'Connor, Taylor, Hanley, Kilgallon, King, Cairney, Gestede, Conway, Rhodes.
Rovers 2nd half: Kean, Green, Henley, Songo'o, O'Connell, Lenihan, Rochina, O'Sullivan, Williamson, Varney, Best.
Goals: Best 56 mins, Rochina 60, 75 mins, O'Connell 88 mins.