After Raza fell short of a deserved century for the second time in the match, Regis Chakabva and Graeme Cremer batted out 190 deliveries for a 49-run partnership that took Zimbabwe to tea on 259 for seven, leading by 137.
With Zimbabwe declining the opportunity to declare during the interval, the game headed into the final session with neither side making a compelling case for why they should win the game.
Malcolm Waller then completed a disappointing series with the bat when he scored just 15 before edging a delivery from legspinner Devendra Bishoo to slip.
But Raza was unmoved, using a review to overturn an incorrect lbw call after he had been given out on 72, before becoming the second player after South Africa's Jacques Kallis to score 80 or more runs in both innings of a Test and take a five-wicket haul.
At that point Zimbabwe were 210 for seven, leading by just 88, leaving the West Indies with an excellent chance of wrapping up the innings and completing a 2-0 series victory.
But Chakabva dug in for an unbeaten 48, while captain Cremer faced 105 deliveries to reach tea on 13 not out.