Ireland need three more wickets to claim their one-off Test against Zimbabwe and make it three successive wins in the longer format.
Andy Balbirnie's men head into the fifth and final day in Bulawayo with the hosts on 183 for seven chasing 292.
Four wickets fell as Sunday's play was curtailed by poor light and bad weather, Ireland left-arm spinner Matthew Humphreys taking three of them as he took his figures for the innings to four for 41.
He accounted for Brian Bennett (45), captain Johnathan Campbell (33) and Nyasha Mayavo (eight), while Barry McCarthy clean bowled Trevor Gwandu in the first over of the day.
Wessly Madhevere's maiden half-century formed the fulcrum of the Zimbabwean response but, with another 109 needed by the home team, he will need to add plenty more to his unbeaten 61 to force a tight finish.
Ireland beat the same opponents in their previous Test in Belfast last July and also defeated Afghanistan in Abu Dhabi five months earlier.
