The veteran striker opened the scoring at Adams Park with a close range finish after the Wanderers had dominated the opening 45 minutes without making the breakthrough.
However, Murphy got on the end of a cross from Sam Wood to level the scores and Wanderers weren't able to force a winner despite some late pressure.
Gareth Ainsworth reverted to the same side that had won 2-0 against AFC Wimbledon last weekend, bringing Steven Craig back into the side after he was benched for the midweek trip to Exeter.
The Blues began brightly under the autumn sunshine and Paris Cowan-Hall forced a save from Mark Cousins before Sam Wood and Josh Scowen sent efforts over the bar in the opening five minutes.
Wycombe continued to press with Steven Craig causing a number of headaches for the visiting defence, and he headed wide before dummying a low cross by Cowan-Hall only for Peter Murphy to be crowded out.
Murphy came close to breaking the deadlock on 15 minutes when Paul Hayes’ superbly dinked cross met the midfielder at the back post, but as he stretched to meet it, his header bounced down off the bar and was cleared by a defender.
A break in play for an injury affected the tempo of the game although Wanderers remained on top, carving open a number of half-chances without really threatening Cousins.
Paris Cowan-Hall was forced off through injury before the break, with Max Kretzschmar taking his place, before Sam Wood’s fierce half-volley was well held by Cousins.
The hosts endured a slightly wayward start to the second period but found their rhythm again when Craig and Hayes combined superbly to tee up Kreztschmar, who bent his shot just wide of the far post from inside the area.
Dagenham’s best chance of the match so far arrived moments later when Damian Batt wriggled free in the box and saw his shot tipped wide by Matt Ingram, before Jamie Cureton fired over from the resulting corner.
The visitors grew in confidence and opened the scoring through Jamie Cureton, a constant thorn in the side of the Wanderers over his lengthy career. Ade Yusuff escaped in the box, not for the first time in the game, and although his shot was blocked by Alfie Mawson, the veteran striker was in the right place to tap home.
The goal woke Wycombe from their post-interval slumber and they began to apply the pressure without finding the cutting edge, being well denied by a resolute visiting defence.
But they were powerless to deny the combination of Sam Wood and Peter Murphy which created the goal on Tuesday night and the equaliser in this match, with the former clipping in a perfect cross which Murphy headed home with aplomb.
It set up a potential grandstand finish with the Blues hunting a winner, and the tension got to Daggers manager Wayne Burnett as he was sent to the stands for an act of dissent before Peter Murphy fired over a difficult chance from the edge of the area.
It was the last chance of the game as both sides had to settle for a point, extending Wanderers’ unbeaten home run stretching back to the middle of August.
Wycombe: Ingram, Jombati, Jacobson, Mawson, Pierre, Cowan-Hall (Kretzschmar 42), Murphy, Scowen, Wood, Craig (McClure 74), Hayes.
Unused subs: Richardson, Rowe, Bloomfield, Lewis, Walker.
Dag & Red: Cousins, Batt, Green (Partridge 77), Saah, Doe, Chambers (Goldberg 88), Bingham, Boucaud, Porter, Yusuff, Cureton (Doidge 77).
Unused subs: O’Brien, Connors, Hemmings, Raymond.
Ref: Mr S Mathieson
Attendance: 3,316 (127 from Dagenham)
Winning 50/50 Draw number: 120069
Prize Money: £634.50