Both sides went into the game on the back of impressive recent records, with Boro having won their last three while the Tigers had emerged victorious in four successive league games.
Just two places separated them in the table prior to the encounter, with the third-placed hosts, in particular, looking to keep pace with the top two.
And, after the sides largely cancelled each other out, Robson was on hand to deliver a sensational 87th-minute winner, firing an unstoppable 30-yard strike past Peter Gulacsi.
The win left Boro second in the Championship ahead of West Ham's late kick-off at Birmingham, while the Tigers, under the stewardship of caretaker manager Nick Barmby, sit fifth.
Middlesbrough and Hull had won their last games - against Cardiff and Millwall respectively - and, unsurprisingly, named unchanged sides.
It was Boro who had the better of the opening exchanges as Joe Bennett and Faris Haroun combined to cause the visitors problems down the left.
Despite the hosts enjoying the majority of possession, the Tigers created the game's first chance as Matty Fryatt headed just wide.
Hull had another opportunity to take the lead soon after, with Aaron Mclean seeing his effort parried away by Jason Steele.
Middlesbrough, though, were still dominating proceedings, Scott McDonald forcing a save from Gulacsi after good work from Justin Hoyte.
As the half wore on, Barmby's side were starting to show impressive adventure, epitomised by Steele having to be on high alert to turn Andy Dawson's effort around the post.
The second period started in much the same vein as they first as the sides battle for the initiative.
The visitors again were looking the more likelier to score, though Robert Koren could only direct into the hands of Steele after being cleverly found by Liam Rosenior.
Chances were proving increasingly few and far between, which perhaps added to the frustration as Matthew Bates was denied by Gulacsi.
But Paul McKenna was guiltier at the other end, driving horribly wide after neat work from Koren and Mclean teed him up.
Both sides appeared to be settling for a draw as full-time edged ever closer, although Gulacsi again had to be on high alert to keep out Haroun's header.
The Tigers goalkeeper had no answer moments later, though, as Scotland international Robson fired home a brilliant strike from a tight angle.
The visitors battled valiantly thereafter, but the goal proved the ultimate sucker-punch and Boro took the points.