Pompey were one of the division’s biggest spenders this summer after Cook had been lured to Fratton Park from Sky Bet League One club Chesterfield, and new addition Gareth Evans opened the scoring before fellow fresh face Kyle Bennett contributed a second-half brace.
Former Doncaster winger Bennett curled an effort over the top in the first period before Matt Tubbs was denied by a brilliant save from Mark Cousins in the Daggers goal.
Evans fired wide of a post before the half-time interval but Pompey took 51 minutes to finally find the net.
A corner from Bennett was met by Evans’ head and the former Fleetwood winger’s effort went into the goal at the Fratton End.
Ashley Hemmings saw a shot deflected into the side netting at the other end yet Portsmouth doubled their advantage through Bennett, who drifted in from the left and blasted a glorious strike in off the underside of the crossbar.
And another effort from range from Bennett, this one from 25 yards out, completed a memorable afternoon for Cook’s side.