Holder and Dowrich came together with the West Indies reeling on 230 for seven, still 96 runs short of Zimbabwe's first-innings total, after Sikandar Raza tore into the tourists with a maiden five-wicket haul.
They turned the game on its head with a counter-attacking partnership as Dowrich ended Tuesday unbeaten on a career-best 75, while Holder contributed 71 not out.
That saw the West Indies to stumps on 374 for seven, leading by 48 runs.
The record partnership for the eighth wicket at Queens Sports Club took some of the shine off the offspinner's five for 82, which was the first five-wicket haul by a Zimbabwean in Tests at the ground since 2003.
Having contributed 80 in the first innings, Raza was also the fifth Zimbabwean to score a 50 and take five wickets in a Test.
While the second evening had produced attritional cricket as the West Indians crawled to stumps on 78 for one, the tourists were more adventurous on day three with opener Kieran Powell leading the way in a 55-run stand for the second wicket with nightwatchman Devendra Bishoo.
Powell looked destined for a fourth Test century after he was dropped on 85 by Graeme Cremer, but seamer Chris Mpofu ensured the mistake was not costly as he used the second new ball to have the opener caught at gully for 90.
An attacking 56-run stand for the fifth wicket between Shai Hope and Roston Chase put the West Indies back on top after lunch, before Raza intervened once again.
With a large deficit and just three wickets in hand the West Indies looked set to concede a first-innings lead on a difficult pitch, but Dowrich and Holder swung the match back in their favour.
"We're only 48 runs ahead, but we've put lots of miles on their legs," said Powell.
"We're going to come back tomorrow with two set guys, put some more miles on their legs and stretch out that lead as much as possible. Any lead is a good lead on this pitch.
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