Having seen Zimbabwe lose five wickets for 47 runs on the third morning as they replied to Sri Lanka's 537 all out, Moor and Cremer put on 132 for the seventh wicket to stabilise the innings.
Although Moor succumbed to a short ball from debutant Lahiru Kumara to depart for 79 in the afternoon session, Cremer batted on to reach a career-best 62 not out as Zimbabwe went to tea on 291 for seven.
Opener Tino Mawoyo started the trend when he pulled a short ball from Suranga Lakmal straight to the man in the deep to depart for 45, and two overs later Hamilton Masakadza prodded forward to edge Lakmal to slip for 33.
A careless sweep from Sean Williams saw him pick out deep midwicket, and a lack of foot movement accounted for Craig Ervine and Malcolm Waller as they were trapped lbw by Dilruwan Perera.
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The pair were only separated when Kumara produced a quick bouncer that Moor had no answer to, as the batsman fended to slip.
Kumara went on to knock Cremer's helmet off his head and rattle the Zimbabwe skipper, who was fortunate to see his hook shot dropped at deep backward square-leg soon after.
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