Seamus Conneely fired home an equaliser in the first minute of injury time for the visitors, lashing in a rebound from close range after Will Norris made a fine save from Nicky Hunt.
Ryan Bird struck what looked to have been the winner 11 minutes from time, seeing his effort deflected home after substitute Gearoid Morrissey guided a cross into his path.
Tom Elliott had given the hosts an eighth minute lead, heading beyond Scott Davies after running onto Josh Coulson’s high ball out of defence.
Accrington were level six minutes before the interval through Piero Mingoia. Michael Nelson’s attempted clearance hit team mate Greg Taylor, allowing Mingoia to run through and fire past Norris.
Norris had made a good stop to deny Sean Maguire early in the second half, with Josh Coulson bravely blocking the rebound from Josh Windass.
Elliot headed Sullay Kaikai’s free-kick just wide for Cambridge with the last touch of the game.