Daggers were made to rue a late set piece as they made the long journey back from Hartlepool without a point.
James Poole’s fourth of the season gave the hosts an early lead, however, Zavon Hines
did level after a fine piece of play 11 minutes into the second half.
But any hopes of the Daggers picking up a point on their travels went as Monkhouse headed Matty Dolan’s corner past Chris Lewington
after 79 minutes.
Manager Wayne Burnett went with the same starting XI which guided them to success over highfliers Rochdale 3-1 last weekend. Luke Wilkinson
did return to the bench though, after injuring his ankle in the 1-0 win at Southend United.
The hosts, who were also unchanged from their 1-0 loss last time out at Scunthorpe went on the attack from the off and Simon Walton saw his goalbound shot deflected behind for a corner.
The first chance for the visitors saw some excellent play down the right wing for the Daggers before working his way inside, but firing nearer the corner flag than the Hartlepool goal.
However, in fortunate circumstances the hosts took the lead after 12 minutes.
Right back Michael Duckworth drilled a shot on goal, only to see it blocked by Luke James before his shot was tapped in by James Poole from close range.
Pools were still on the ascendancy and Lewington kept out another effort from Walton with his chest after the midfielder drilled a shot goalwards.
In comparison to last season, Daggers have had no trouble scoring this season and Medy Elito
went closest to levelling after 26 minutes from another quick counter attack but his shot was comfortably saved by Flinders.
And they kept up the threat as Hines, who had switched wings with Elito, beat Flinders but Barking-born Jack Baldwin managed to clear it behind for a corner.
Despite not playing their best the Daggers continued to create chances and Luke Howell
spurned another good opportunity as he shot wide from 20 yards after creating some room for himself just outside the box.
Burnett opted to keep things as they were at the start of the second period and 10 minutes in they found the leveller with a fine individual effort from Hines as he came in off the right wing and shot low past Flinders.
That gave Daggers the spark they needed and they should have been leading on the hour mark when Elito played in Murphy who beat the offside trap.
But rather than taking on the effort himself he opted to square for Abu Ogogo
but his shot was deflected behind for a corner.
In an open second period Hartlepool went on the attack and had Lewington to thank for keeping out Duckworth’s effort from just outside the box.
There were chances galore and Ogogo and Brian Saah
went close within a matter of seconds.
The Daggers skipper saw a flicked effort from Billy Bingham
’s free-kick cleared for a throw and from a ball in Saah’s header fell narrowly wide of the target.
Defending from set pieces had initially been a problem for the visitors this season, and it reared its ugly head once again as the Pools took the lead after 79 minutes.
Matty Dolan put a corner into the box and Monkhouse headed home.
Burnett brought on Chris Dickson and Afolabi Obafemi
in search of a late leveller and despite four minutes of time added on the Daggers slipped to defeat.
Dagenham & Redbridge:
Lewington, Connors, Doe, Saah, Hoyte, Ogogo, Howell (Dickson 81), Bingham, Elito (Obafemi 89), Hines, Murphy.
: Wilkinson, Ilesanmi, Scott, Shields, Seabright.
3,450 (99 Daggers fans)