Hasselbaink's first-half double took his tally for the season to 12 with eight of them coming in the last nine games.
Albion's comeback hopes disappeared nine minutes into the second half when Scottish international midfielder Nigel Quashie was dismissed by referee Mike Dean for kicking out at George Boateng.
Hasselbaink's explosive run in front of goal has coincided with the upturn in Middlesbrough's fortunes that has seen them reach the quarter-finals of the FA Cup, the last 16 of the UEFA Cup and boost their Premiership survival hopes.
This latest win moved them five points clear of fourth from bottom Albion with a game in hand.
Their revival is something that Albion can only dream about as they face up to another tough battle to avoid the drop.
Crushed 6-1 at Fulham in their previous game, Albion had been on a break in Dubai in a bid to recharge their batteries.
But the trip failed to have the desired effect as Albion slipped to their third defeat in five games - taking just four points from a possible 15 in the process.
They are now just three points clear of third from bottom Birmingham City who have a game in hand on them.
Albion felt hard done by to be trailing at half-time as there was a touch of controversy about both of Hasselbaink's strikes but that was of little concern to Middlesbrough.
Albion were convinced that the Dutchman was offside when he collected a 17th minute throughball from Boateng.
But the assistant referee's flag stayed firmly down by his side and Hasselbaink raced 30 yards before drilling home a low shot despite the best efforts of goalkeeper Tomasz Kuszczak.
It was a goal that was somewhat against the run of play as Albion had peppered the Middlesbrough goal without every seriously testing goalkeeper Mark Schwarzer.
The Australian comfortably dealt with efforts from Neil Clement and Diomansy Kamara while Kanu had a shot blocked and Jonathan Greening fired wide.
Failure to take advantage of the pressure that they created came back to haunt Albion a minute before half-time when Hasselbaink made and scored the second goal.
Once again, Albion were left fuming by the strike after the referee ruled that central defender Curtis Davies had fouled Hasselbaink on the edge of the area.
Davies was adamant that he had won the ball but his protests were waved away. Hasselbaink's free-kick was poorly hit and straight at the wall but it took a wicked deflection off Albion midfielder Ronnie Wallwork and flew past a bemused Kuszczak.
To their credit, Albion refused to go down without a fight but it was always going to be an uphill struggle once Quashie saw red following his midfield tussle with Boateng.
Greening flashed a shot wide on the hour and Kanu forced Schwarzer into a smart save after 77 minutes but Middlesbrough were more than content to sit back and soak up the pressure as they eased to their second successive Premiership win.