The 24-year-old midfielder, who joined Pompey on a summer free transfer from AS Monaco, was making only his second start since late August.
But his close-range header from a corner by Ricky Holmes on the stroke of half-time brought Pompey three desperately needed points and their first win since beating Exeter 3-2 in early November.
Manager Richie Barker, who summonsed his players to a three-hour Christmas Day training session, saw his charges enjoy the lion's share of first-half possession without seriously threatening the Dagenham goal until Padovani scored.
Patrick Agyemang bungled a good chance, while Ricky Holmes became an increasing influence in his wide role, eventually setting up the winner.
Chris Dickson twice wasted chances for Dagenham, who had Pompey increasingly on the back foot as they pressed forward without reward in the second period.
Goalkeeper Trevor Carson made one fine save to deny Scott Doe, but Dagenham generally lacked a cutting edge to save the game.