The home side lost Dean Holden with a slight hamstring strain and Craig Disley with a black eye and concussion in the opening half hour.
But Danny Taylor released Kelvin Langmead and his cross was controlled by Steve Leslie, who beat Tony Roberts with an overhead kick. The Daggers, who saw Scott Doe dismissed in the 70th minute, staged a late fightback but Shrews held firm to claim the points.
Simpson said: "We were really good in the first half. Unfortunately we were against 10 men for the second week running and they got some momentum but we dealt with it better this time.
"Hibbert was absolutely fantastic. He won his headers and worked incredibly hard and was well backed up by (Jake) Robinson. We came back well after a brilliant goal from Benson and against a very, very good Dagenham side."
Source: Team Talk
Source: Team Talk