West Indies began the day on 49-3 with Campbell and Blackwood unbeaten on 28 and 17 respectively.
In the third session of Day 3, Khaled breathed life into the dull contest by striking thrice inside his second over to reduce West Indies to 9-3.
But Campbell and Blackwood removed the early jitters with an unbeaten 40-run stand on Day 3. They began from where they left off the previous day on Sunday and finished the job inside 30 minutes of the morning session.
Previously, Bangladesh were bundled out for just 103 in their first innings. Skipper Shakib Al Hasan top-scored with 51 while six of their batters departed without bothering the scorers.
West Indies took a commanding 162-run lead after posting 265 in their first innings. Skipper Kraigg Brathwaite led the way for the Caribbeans with a patient 94.
Bangladesh were at risk of losing the match by an innings margin after getting reduced to 109-6 in their second innings. A 123-run stand for the seventh wicket between Shakib and Nurul Hasan saved the Tigers from that ignominy.
Kemar Roach broke the stand and also claimed a five-wicket haul to bowl out Bangladesh for 245.
Shakib and Nurul made 63 and 64 respectively.
Roach was named player of the match for finishing with match figures of 7-74.
Both teams will now go to St Lucia to play the second and final Test of the series.