The visitors were 126 for five at tea on day three, with Raza (45) and Peter Moor (30) putting on an unbeaten 67-run stand for the sixth-wicket a the R Premadasa Stadium.
Raza lifted Zimbabwe from a precarious 23-4, followed by 59-5, after Sri Lankan left-arm spinner Rangana Herath rattled the visitors' top-order with four wickets.
Herath, who got three wickets in the second session of play, bowled Sean Williams for 22 as Zimbabwe teetered dangerously close to losing their 10-run advantage.
But it was Herath's left-arm spin that undid the fine work from leg-spinner Cremer (5-125).
Off-spinner Dilruwan Perera joined forces to get the prized wicket of first-innings centurion Craig Ervine for five at the stroke of lunch.