Chase's off-spin was instrumental in triggering a collapse as Bangladesh slumped to 6-79 and a lead of only 106 in the second innings at stumps on Friday after an early finish due to bad light.
Left-arm spinner Jomel Warrican, who had figures of 5-53 in the first innings, took 2-19 to back up his skipper with the Test still in the balance.
The West Indies conceded a 27-run first-innings lead but pace bowler Shamar Joseph struck in the second over of Bangladesh's reply, dismissing opener Tanzid Hasan for a duck.
Chase then removed Shadman Islam, the centurion in the first innings, for 13 and Towhid Hridoy for two in the space of three balls. Then Chase took out counterpart Najmul Hossain Shanto on 10.
Warrican sent back Liton Das, trapping him lbw for four, leaving Bangladesh at 5-35.
Warrican also broke the brief resistance of Mehidy Hasan Miraz by rattling his stump on nine as Bangladesh were reduced further to 6-53.
Jaker Ali and Nayeem Hasan were both on 18, having begun to revive the innings, Â when play was called off for the day.
Jaker came into the side as a concussion substitute for Mominul Haque, who received a blow on his head while fielding at short leg.
Nayeem earlier returned figures of 4-33 with his off-spin to bowl West Indies out for 245 after the visitors resumed at 4-134.
Tagenarine Chanderpaul's stubbornness rewarded him with his third half-century from 164 balls when he flicked Taijul Islam for a single.
However, soon after his laborious fifty, he edged a delivery off pacer Shoriful Islam to second slip, ending a 65-run partnership with Justin Greaves for the fifth wicket.
Chanderpaul played 184 balls for 56 runs that included six fours and one six.
After Chanderpaul's departure, Greaves and Chase looked solid in the crease as they took the side past 200.
But Nayeem dismissed Greaves on 46 and followed with the wickets of Shamar Joseph and Warrican to confirm Bangladesh's first-innings lead. Chase was left stranded on 43.
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