Picking up from where he left off the previous evening when he took two wickets in two overs, the tall off-spinner added four more victims to finish with innings figures of six for 49 -- and a match analysis of nine for 107 -- as the visitors were routed for 107 in their second innings just before lunch.
Left with the academic task of scoring 12 runs for victory, debutant seamer Tendai Chatara claimed the wicket of Kieran Powell to a catch at gully, delaying the formality of victory until after the interval when Chris Gayle hit the winning runs.
Following 2-0 series triumphs at home to New Zealand last July/August and in Bangladesh last November, this result gave the West Indies five consecutive Test wins for the first time since the all-powerful squad led by Viv Richards completed the feat in 1988.
They will now be heavily favoured to make it six in a row at the expense of a Zimbabwean side woefully short of international exposure at this level.
"We did exactly what we wanted to do, win our fifth Test in a row, everybody played their part really well," said West Indies skipper Darren Sammy, who smashed his team's top score of 73 in the first innings of 307.
"Now we have a chance to make it six in a row, something that hasn't happened for over 20 years."
Struggling Zimbabwe captain Brendan Taylor admitted his team have plenty of work to do ahead of the second Test in Roseau from March 20.
"It was a tough Test, we let ourselves down in the first innings," Taylor said.
"Getting just 200 was disappointing, had we got 300 it could have been a different game."
Shillingford, who was named man of the match, wasted no time at the start of the third day, having struggling captain Brendan Taylor caught at short-leg for six in the first over.
Kemar Roach knocked out the middle stump of the other overnight batsman, Ray Price, in the next over to reduce Zimbabwe to 47 for five.
When Malcolm Waller fell to another close-in catch by Powell, his fifth of the match, off Shillingford, it appeared that the West Indies would have completed an innings victory with the score at 58 for six.
At that stage, Zimbabwe were still 38 away from making the home side bat again.
However an unbeaten 23 from Craig Ervine at least ensured that indignity was avoided, and while Shillingford accounted for Regis Chakabva and Graeme Cremer among the lower order, it was left to fast bowler Shannon Gabriel to polish off the innings with the wickets of Kyle Jarvis and Chatara in the space of three deliveries.