Adam Cunnington opened the scoring in the first half turning in Stuart Sinclair’s shot before Murphy lashed home a shot from a Dover corner to make the game 1-1.
September’s Manager of the Month Darrell Clarke made three changes to the side that drew at Eastleigh on Tuesday night.
Will Puddy starts in goal, replacing the suspended Steve Mildenhall. Dave Martin and Adam Cunnington come into the side replacing the suspended Ollie Clarke and with Ellis Harrison dropping to the substitutes bench.
The home side started in a positive way and Adam Cunnington could have opened the scoring inside 10 minutes.
Recalled to the starting 11 after missing out on Tuesday night Cunnington lept highest to latch onto the end of Lee Brown’s cross.
The Cambridge loanee headed the ball goalwards only to be denied by the crossbar with Dover keeper Andrew Rafferty rooted to his line.
Dover hit the woodwork themselves inside the opening 20 minutes as Stefan Payne struck the inside of the post from the edge of the area.
The home side could have been reduced to 10 men moments later as a poor back pass from Neal Trotman allowed Ricky Miller through onto goal.
Miller collided with Will Puddy in the Rovers penalty area but referee Wayne Barratt waved away Dover’s protests allowing Tom Parkes to clear the danger.
Rovers took the lead just past the half hour mark as Adam Cunnington scored his third goal in the blue and white quarters.
Lee Brown took his throw in quickly and found Dave Martin on the touchline, Martin’s cross into the box was cleared but only to Stuart Sinclair on the edge of the area.
Sinclair lashed a shot towards goal that was going wide before Cunnington diverted it past Rafferty to open the scoring.
Dover started the brighter of the two sides in the second half and Chris Nanetti tried his luck from distance however, Will Puddy was equal to it and pushed it behind for a corner, which Rovers easily cleared.
Tom Parkes had a chance to double Rovers lead 10 minutes into the second half but headed a Dave Martin corner over the top of the Whites goal.
Just before the hour mark Dave Martin burst through the middle of the pitch and past two Dover defenders before picking out Cunnington on the left hand side of the area.
Cunnington looking for his second of the game decided to shoot but lashed his effort high and wide of Andrew Rafferty’s goal.
Dave Martin continued his impressive second half moments later putting an inch perfect ball across the six yard box which Dover defender Tyrone Sterling could only turn behind for a corner.
Martin took the corner short before putting the ball into the penalty area, Lee Mansell latched onto a loose ball in the box but his shot was blocked well by Richard Orlu.
Substitute Ellis Harrison linked up well with Tom Lockyer down the Rovers right before playing in the young fullback who could only dribble his shot at Rafferty
Rovers had a great chance to double their lead with 15 minutes remaining as Matty Taylor was put clean through onto goal but only managed to find the feet of an outrushing Andrew Rafferty.
Dover had a chance to snatch a point at the death but substitute Nick Deverdics thumped his shot over Puddy’s crossbar to the relief of everyone in the stadium.
Rovers were made to pay going into stoppage time as Whites substitute Tom Murphy made no mistake firing a shot into the top right of the Rovers goal.
Both sides pushed for a winner before referee Wayne Barratt blew his whistle for full time.
Up next for Rovers is Dartford at the Memorial Stadium on Tuesday night before an away trip to Aldershot on Saturday.
Rovers: Puddy, Lockyer, Trotman, Parkes, Brown, Gosling (Monkhouse – 71), Mansell (C), Sinclair, Martin, Cunnington (Harrison – 69), Taylor.
Unused Substitutes: Preston (GK), McChrystal, White.
Dover: Rafferty, Stone, Orlu, Lock, Payne (Reid – 54), Sterling, Nanetti, Bonner (Murphy – 84), Miller, Taiwo (Deverdics – 69), Essam.
Unused Substitutes: Kinnear, Raggett.