The Durham keeper-batsman gave himself the perfect 25th birthday present with his second century for Ireland - the other coming against Sri Lanka in Belfast last year.
Poynter struck 18 boundaries in his 125 from 166 deliveries, sharing a second wicket stand of 101 with Andrew Balbirnie (44).
Balbirnie had come to the crease following the dismissal of Paul Stirling (20) and found the boundary ropes six times in an entertaining innings - ended when harshly adjudged lbw off the bowling of M'Shangwe.
Poynter continued to impress - dominating a third wicket stand of 90 with Niall O'Brien (21) before both fell within the space of six balls with the total on 212.
Stuart Thompson (4) fell cheaply, but a 6th wicket partnership between Gary Wilson (47) and Kevin O'Brien (22*) looked to have given the Irish the upper hand before Wilson fell to the final ball of the day.
Earlier John Mooney (4-74) and Craig Young (4-107) finished with four wickets apiece as Zimbabwe added 40 runs to their overnight 352 for 6 - Malcolm Waller the last wicket to fall for a magnificent 138.
Ireland resume day three exactly 100 runs adrift, but with batting strength in depth will be confident of parity.
Meanwhile in Malaysia, Ireland's Under 19 cricketers made it two wins from two after a comprehensive 8 wicket win over the USA. Three wickets for Aaron Gillespie, and two each from the Phoenix pair of Rory Anders and Ben White saw the States dismissed for exactly 100.
That modest total proved no trouble for the Irish - skipper Jack Tector making a Man of the Match 60 as they passed their target in just 15.4 overs. The Irish are back in action tomorrow (MON) when they take on Uganda.
ZIMBABWE A v IRELAND
Day 2 of 4,
At Harare Sports Club,
ZIMBABWE A 392 all out (102.3 overs, M Waller 138, R Chakabva 104, PJ Moor 52, H Mazakadza 28, G Mamhiyo 22, T Garwe 21, J Mooney 4-74, C Young 4-107)
IRELAND 292/6 (74.2 overs, S Poynter 125, G Wilson 47, A Balbirnie 44, K O'Brien 22*, N O'Brien 21, P Stirling 20, B Vitori 2-56)
Continues Monday at 9am (BST)