A hopeful ball into the Wycombe box appeared to strike Leon Johnson on the hand and the referee had no hesitation in pointing to the spot. Rainford coolly converted the resulting spot-kick.
The home side had moments earlier been given a real scare when Johnson slipped inside his own box and Ben Strevens' shot was brilliantly parried away by Frank Fielding.
Wycombe had started the game as the brighter of the two sides and could have taken the lead on three occasions inside the opening 15 minutes.
First Gary Holt saw his shot from 25 yards creep just past Tony Roberts' left-hand post, then John Sutton missed a golden chance, tamely volleying straight at Roberts after hesitation in the visitors' defence had let him in.
Top scorer Scott McGleish then saw his volley sting the Dagenham stopper's palms after good work by Sergio Torres.
The hosts continued to press for an equaliser in the second half but found Roberts in great form, saving brilliantly to deny Sutton's close-range flick from a Craig Woodman cross and then McGleish latched on to another Sutton header, but shot straight at the veteran keeper.
Rainford almost grabbed his second of the match but Fielding excellently tipped away the midfielder's header from a Glen Southam corner and despite throwing on substitute Leon Knight as a third striker, Wycombe were unable to break down the visitors' defence.