The tourists posted 448 all out in their first innings before reducing Zimbabwe to 140 for four at the close of play, a lead of just 18 runs for the home side with six second innings wickets remaining.
Zimbabwe have mounted something of a recovery, though, with Sikandar Raza (58 not out) and Peter Moor (39 not out) putting on an unbeaten stand of 94 for the fifth wicket.
Dowrich (103 from 232 balls) had earlier scored his maiden test ton as he put on 212 for the eighth wicket with Holder (110 from 198 balls) as West Indies claimed a 122-run first innings lead.
It is the first time since 1908 that numbers eight and nine have scored centuries in the same test innings.
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Zimbabwe off-spinner Raza (five for 99) recorded career-best bowling figures, while seamer Tendai Chisoro bagged the last three wickets of the innings for figures of three for 113 on his debut.
West Indies won the first test at the same venue by 117 runs and will be looking to secure the series on Thursday.
(Reporting By Nick Said; Editing by Christian Radnedge)
