Murphy converted from the spot to double the lead, and despite their numerical disadvantage Blues more than matched their hosts, but struggled to create many clear-cut chances with Gary Doherty's header, which rebounded back off the post, the closest they came.
Gareth Ainsworth made five changes to his side with Charles Dunne, Leon Johnson, Paris Cowan-Hall, Max Kretzschmar and Matt McClure coming in.
Sam Wood missed out with a tight groin, while only six substitutes were named as Billy Knott was forced to withdraw from the squad late on through illness.
Wanderers started well with Cowan-Hall looking a threat down the right and they created the first-half chance in the ninth minute. Kretzschmar’s clever free-kick found McClure at the far post, but no-one could get on the end of the striker’s header back across goal and Dagenham scrambled clear.
The Daggers’ top scorer Murphy threatened to break through in the 21st minute, but he slipped and Anthony Stewart cleared. However, they were to take the lead three minutes later.
Obafemi received the ball in the area and he was allowed to turn too easily before firing past Matt Ingram and into the far corner. The shot was the first from either side as the opening quarter of the game was predominantly fought out in midfield.
Murphy shot wide from a tight angle after being released down the right in the 29th minute as the goal buoyed the hosts. However, Kretzschmar was the next to try his luck, only for his 25-yard free-kick to fly over the bar.
Stewart thought he had levelled from Kretzschmar’s cross five minutes before the break, but his fine header was ruled out for a foul.
Ainsworth was forced into his first change a minute later as Craig had been unable to shake off a shoulder injury he picked up midway through the half and was replaced by Dean Morgan.
Lewis half-volleyed wide against his former side after good work from Scowen, before only a fine last-ditch challenge prevented Morgan from getting a shot off six yards from goal.
Wanderers finished the half firmly in the ascendancy and only a superb late challenge from Scott Doe denied McClure a clear goal-scoring opportunity in injury-time.
Blues’ task became even harder 60 seconds after the restart. Medy Eliot released Murphy through the middle and Stewart made what initially looked like an inch-perfect challenge. However, referee Keith Stroud thought otherwise and awarded a penalty as well as sending off the centre-back. Murphy made no mistake from the spot, sending Ingram the wrong way to double the lead.
Dagenham had a goal of their own ruled out in the 51st minute as Zavon Hines was in an offside position when he slotted home a rebound.
McClure’s strike was deflected behind by Brian Saah after a forceful run from Scowen and the striker then did well to close down Lewington, who crashed a clearance off the forward, only for the ball to go wide of the post.
Luke Howell could have wrapped up the points for the hosts in the 63rd minute, but he volleyed high over the bar after Ilesanmi burst into the area.
Lewington produced a superb stop to parry away Cowan-Hall’s stunning 20-yard volley after McClure had done well to head the ball down to the winger. Doherty headed the resulting corner after eluding his marker.
Junior Morias was introduced seven minutes from time and Chairboys were inches away from setting up a grandstand finish. Doherty outjumped his marker to meet McCoy’s cross and his header beat Lewington, only to rebound back off the post.
Wanderers: Ingram, McCoy, Dunne, Stewart, Johnson, Cowan-Hall, Scowen, Lewis (c), Kretzschmar (Doherty 50), McClure (Morias 83), Craig (Morgan 41).
Subs: Horlock, Arnold, Bloomfield.
Dagenham: Lewington, Hoyte, Ilesanmi, Doe, Saah, Ogogo (c), Howell, Elito (Edgar 80), Hines, Murphy (Scott 90), Obafemi (Saunders 54).
Subs: Seabright, Wilkinson, Dickson, Connors
Attendance: 1,618 (361 Wycombe)