West Indies reached 144-5 at stumps on the fourth day,
needing only seven runs to avoid follow-on after Bangladesh had declared first innings on 350-9 three overs into the second session.
As rain and a damp outfield caused the cancellation of more than two days’ of play, enforcing a follow on was the only option for Bangladesh to create an outside chance of a win.
Sunny raised the prospect with his dream debut, but veteran Shivnarine Chanderpaul brought his all experience together to deny them any chance and take West Indies close to safety.
Bangladesh also had themselves to blame as a number of catches went down which could have made the situation completely different.
A couple of umpiring decisions went against them while on one occasion batsman survived for no-ball despite seeing his two stumps uprooted.
A combination of all these things made a draw an obvious result in this Test, though it will not do any harm to the cause of Sunny, who will remember the Test for the rest of his life.
It is not just because he has got his Test cap in this game but for the performance he put in which also gave Bangladesh a great hope to have a spinning partner for Sakib al Hasan in the longer version.
It all, however, began on a wrong note.
Rubel Hossain uprooted two wickets of Kraigg Brathwaite in the second over only for the umpire to signal a no-ball. Thanks to Shahadat Hossain, who forced Lendl Simmons to give a catch to Roqibul Hassan at gully, they, however, did not have to wait too long.
But Shahadat was almost ruining the advantage of early breakthrough when he dropped a simple catch of Kirk Edwards on naught in what was only the second ball of Sunny in Test cricket.
Mushfiq gave Edwards his second reprieve on 16 off Sunny to prompt the bowler to take the matter in his own hands as he trapped the batsman in front two balls later for his first Test wicket.
Sunny also had Darren Bravo after the tea break to leave West Indies reeling at 52-3 before Chanderpaul and Brathwaite provided the first resistance with a 62-run fourth-wicket stand.
Chanderpaul also survived two close appeals and was almost caught at forward short-leg by Imrul Kayes off Sunny on 26. After an initial jittery Chanderpaul launched a counter-attack hitting Sunny for two sixes off successive balls to force Bangladesh to spread their fielding.
Brathwaite’s luck finally ran out at 33 when Imrul managed to take a catch giving Sunny his third wicket. The defiance of Chanderpaul (49) also came to an end shortly with Shahriar Nafees taking the catch at slip.
Marlon Samuels (17 not out) was batting with Carlton Baugh (six not out) at the stumps.
Earlier resuming at 255-4, Bangladesh lost a wicket without scoring a run when skipper Mushfiq got the leading edge off a Fidel Edwards short-pitched delivery and was caught by Bishoo at square leg.
Mushfiq, unbeaten on 68 overnight, was only facing his first ball of the morning session.
Shahriar Nafees (32), who had retired hurt after an Edwards bouncer hit him in the face on the opening day, resumed his innings but could add only 11 runs to his score before departing.
Edwards took the wicket of Nafees, who slashed and edged a catch to wicketkeeper Carlton Baugh.
Debutant Nasir Hossain survived some deadly bouncers and yorkers from Edwards to score 34 off 47 balls with six fours before Baugh took a skier off Bishoo to send him back to the pavilion.
Bishoo later claimed the wicket of Sunny and Shahadat to return with 3-81.