The forward, who lined up on the left for the visitors, did most of his good work down the middle.
Adam Hammill had given Huddersfield an early lead but Adomah pounced on a poor back pass to level.
A fine curled shot by Nahki Wells had put Huddersfield back in front before the break but Adomah grabbed his second early in the second period with a rising shot which ensured his side a share of the points.
The draw left both teams still looking at the wrong end of the table and was just reward as neither looked to settle for a point in front of 11,999 spectators.
Huddersfield got off to the perfect start when Hammill shot in from the left edge of the area after the home side had won the ball in midfield in the third minute.
Oliver Norwood fed Hammill who finished coolly past Dimi Konstantopoulos for his fourth league goal of the season.
The visitors had a chance to respond shortly after when Huddersfield failed to clear and Adomah pulled back for Jacob Butterfield but he shot over from the edge of the area.
Middlesbrough were level after 10 minutes when a back pass from Oscar Gobern set up Adomah and he rounded Alex Smithies before slotting the ball into the empty net.
Gobern nearly made amends but his cross from the left was just too far in front of the head of Danny Ward.
Wells thought he had put Huddersfield back in the lead but he was marginally offside as he ran on to Gobern's pass before shooting past Konstantopoulos.
Captain Peter Clarke headed just over on the half hour from a Hammill corner as the home side continued to push for a second.
Wells gave them that goal with a fine finish in the 34th minute.
The January signing from Bradford cut in front the right and curled a left-footed shot form the corner of the area over the despairing dive of the keeper and in off the far post.
Wells then turned provider as his through ball found Ward but his shot from a tight angle was beaten away by Konstantopoulos.
Ward was close to a third goal when he advanced and shot from 25 yards but his effort flashed just wide of the far post.
Gobern shot just wide of the keeper's right hand post following Hamill's cross from the left as Huddersfield searched for the third goal their dominance deserved as half-time approached.
Huddersfield had started the first half well but it was Middlesbrough who matched their opening in the second period to restore parity for a second time.
Huddersfield were punished for losing the ball in midfield and it was once again Adomah who made them pay, this time in the 47th minute.
He claimed possession and hit a fine rising shot past Smithies to again draw his side level.
Adam Clayton's persistence fashioned an opening for Hammill but after cutting in from the left his right-footed shot was well over the bar.
Norwood and Clayton set up Ward and Wells with searching long balls but nothing came of either opening as Huddersfield continued their recovery from such a poor start to the half.
Norwood's ball from the right was too deep for Hammill at the far post as Huddersfield again failed to make their dominance tell.
Manager Mark Robins was booed for taking off Wells and bringing on James Vaughan with a little over 10 minutes to go.
But try as they might Huddersfield could not find a third goal which would have given them the victory they probably deserved.