It was another impressive rearguard display from Aitor Karanka's men but toothless Boro have scored only three league goals in the new year. Their late charge to the play-offs is faltering as a result, while Blackburn missed the chance to go seventh.
Mustapha Carayol was the main tormentor for a lacklustre Rovers side but found Robinson an immovable object in the visiting goal, with substitute Albert Adomah also thwarted in his late attempt to plunder all three points.
Striker Danny Graham - whose first start for Boro came nearly eight years ago, four days before the club's losing appearance in the 2006 UEFA Cup final - was handed a second home debut following his deadline-day loan switch from Sunderland.
Boro would dominate the first half and showed their determination to end the goal drought as soon as possible.
Carayol's first effort was hooked away by Tommy Spurr but, from the resulting corner, on-loan Chelsea midfielder Nathaniel Chalobah forced a low one-handed save from Robinson.
Rovers' chances were limited thanks to an alert and organised Boro defence but Shay Given did well to cover for a rare lapse in concentration as Jordan Rhodes latched onto a ball over the top.
Boro quickly resumed exploiting the left wing through the ever-impressive Carayol.
After his early cross skipped beyond Graham, he combined brilliantly with George Friend to give Robinson another scare. The former England keeper kept the Gambian winger out, though, and did well to smother an effort from Grant Leadbitter.
Blackburn's best early chance came shortly after the half-hour mark as Rudy Gestede combined well with Rhodes to win a corner.
The ball was swung into the area where Gestede took possession, only to blast inches wide of Given's goal.
Graham, who had previously cut an isolated figure in the lone striker's role, looked lively immediately after half-time and twice came close to heading an overdue opener.
Grant Hanley's quick-thinking block on Friend's dangerous cross then left the under-siege Robinson backpedalling to the far post.
Boro sensed blood in the water and went even closer to notching, again through Carayol, with a swift counter-attack allowing Graham to steer his new team-mate into a one-on-one with Robinson.
However, the veteran keeper steeled himself to give his side every chance of snatching victory in the final 30 minutes.
Adomah - on for Emmanuel Ledesma - was next to test Robinson as he loped onto the D to sting the stopper's fingertips.
The ex-Bristol City man later fired tamely down Robinson's throat and, with rain beginning to fall as time ticked away on Teesside, Carayol and Graham were both withdrawn with Boro seemingly content to ride out the stalemate for yet another week.