In a nervy afternoon Dougie Imrie missed a couple of chances for the New Douglas Park side before his Dutch team mate drove past Jakub Divis from just inside the box in the 38th minute - to earn Hamilton their first home league win of the season.
Two minutes before the interval Easter Road defender Francis Dickoh was sent off for picking up his second yellow card for a foul on Hasselbaink.
Accies failed to take advantage of the extra man after the break as they missed numerous chances, but Hasselbaink's goal was enough to take Billy Reid's men to within three points of second-bottom St Mirren with two games remaining, thus ensuring a tense final week of the league season.
Both sides wore black armbands to commemorate the recent death of former Hibernian boss Eddie Turnbull.
The visitors started the game with some purpose and David Wotherspoon and Akpo Sodje both had efforts which missed the target.
Midfielder Liam Miller should have put Hibs ahead in the fifth minute when he was set up by Ricardo Vaz Te, who had capitalised on some slackness in the Accies defence to race down the right.
However, despite having time and space, the former Celtic midfielder side-footed his shot from 12 yards wide of the target.
Hamilton took time to get in to the game. In the 20th minute Imrie had a poor shot easily saved by Divis before Vaz Te fired wide at the other end.
The game remained rather low key but in the 25th minute Imrie had a better effort from a 25-yard free-kick saved down at his left-hand post by Divis.
Sheer endeavour saw Hamilton force their way forward but as the ball flashed across the box on several occasions there were no takers.
However, on the half-hour mark John Chambers' cross from the left found Imrie standing unmarked 10 yards from goal, but he failed to connect properly with his volley and Divis smothered.
Moments later Accies midfielder Gary McDonald tried to set up a team-mate with a header from David Buchanan's cross when he should have tried to get his effort on goal, and the ball was cleared.
But in the 38th minute Accies got the goal their pressure deserved when the bustling Hasselbaink gathered McDonald's headed pass and, from just inside the box, turned to fire past Divis with the ball going in off the far post.
The home side were handed a further boost two minutes from the break when Hibs were reduced to 10 men.
Dickoh, booked earlier for a foul on Imrie, received his second yellow card from referee Mike Tumilty for a foul on Hasselbaink leaving Colin Calderwood's side with an even more difficult task after the break.
Accies were cheered off at the interval by their long-suffering fans who were retaining hope of avoiding the drop.
The home side went looking for the second goal when the game resumed and in the 51st minute Divis made another good save, this time from Ali Crawford's stinging drive.
There was some controversy in the 56th minute when Vaz Te was booked for diving after a challenge by pondering Accies keeper Tomas Cerny on the right-hand side of the box.
Hibs then applied some pressure as the Hamilton defence wobbled and their fans retreated in to a state of some agitation.
In the 65th minute Crawford cracked the bar from 16 yards with a drive after he had been set up by Hasselbaink.
Crawford had another great chance in the 72nd minute when he only had Divis to beat after being put in by Imrie but this time he drove straight at the Hibs keeper from 14 yards.
As Accies pushed for the clinching second goal Divis tipped a Simon Mensing header over the bar for a corner, which the visitors survived.
News of a goal for Inverness against Accies' relegation rivals St Mirren lifted the home crowd and the players responded but the second goal would not come, despite several chances.
However, Hasselbaink's goal proved enough for the win and to keep Accies in with a chance of beating the drop as the pressure increased on the Buddies.