It was just the third time that a World Cup game has ended in a tie but Ireland, playing their first match at the tournament, were far happier with the result after clawing back from what looked a certain defeat.
"In certain stages of the game we did our very best to throw it away then we fought back in the last eight to 10 overs and really gave ourselves a chance," said Ireland's Australian-born captain Trent Johnston.
"I'm very proud of the guys that were out there... the whole squad are a bunch of fighters and we never give in till the game is over."
In 1999, the scores were tied in Australia's semi-final against South Africa, who also ended level with Sri Lanka in a pool match in Durban in the 2003 tournament.
Jeremy Bray had scored an unbeaten 115 for Ireland, Zimbabwe looked to be comfortably heading towards victory.
Half centuries from Vusi Sibanda and Stuart Matsikenyeri left them needing just 12 runs to win off the last four overs with four wickets remaining.
But Ireland captain Trent Johnston gave just two away from a tight over and then Andre Botha trapped Gary Brent leg before and conceded just a single in his over to leave Zimbabwe needing nine off the last two overs.
The next over was a disaster for the African side with captain Prosper Utseya hitting a full toss from Kevin O'Brien straight into the hands of Eoin Morgan at extra cover.
In came tail-ender Christopher Mpofu who failed to score from four balls, with Matsikenyeri trapped at the non-striker's end. Then off the last ball of the over Mpofu was run out attempting a single which his partner had no intention of taking.
Suddenly Zimbabwe needed nine off the final over with just one wicket remaining but at least they had their top scorer Matsikenyeri facing the strike.
The only member of the Zimbabwe side to have previously appeared in a World Cup took two each off the first two balls of off-spinner Andrew White's over but then a single left number eleven Ed Rainsford facing the strike although he managed to scamper a single.
The penultimate ball of the game had Matsikenyeri back on strike and he cracked a short ball from White straight at Johnston who dropped the chance and in the chaos, the Zimbabwean batsmen managed to take two runs and bring the scores level.
Matsikenyeri missed the final delivery though and amidst appeals for a stumping, non-striker Rainsford was run out leaving the scores level and Ireland celebrating.
"Who knows, we may even qualify for the next stage," quipped a jubilant Johnston.
Hosts West Indies and Pakistan are the other teams in Group D.