The 41-cap England international withstood heavy pressure from Boro, who were desperate to score their first goal in four games and revive an unlikely surge towards the play-off places.
Robinson repelled the determined Mustapha Carayol on numerous occasions while thwarting substitute Albert Adomah towards the end of a frustrating afternoon for the hosts at the Riverside Stadium.
An 11th clean sheet of the season saw Rovers take a point home to Lancashire, one that manager Gary Bowyer insisted had been hard-earned by his whole team, although he could not help but single out one player in particular.
"Robbo was outstanding," he said. "He was excellent, he just oozed international class.
"He's always got that in his locker. You don't play for your country as often as he did without having some outstanding ability and you've just seen that today.
"When called upon he did his job magnificently well but then again he's got another 10 in front of him that helped keep a clean sheet.
"The character and resilience that they showed can only be applauded."
Had Rovers converted one of their few chances - Rudy Gestede shot narrowly wide in the first half while 16-goal striker Jordan Rhodes missed the mark late on - Bowyer would be celebrating moving above Brighton and Ipswich and into seventh place.
As it stands they are four points off sixth-placed Reading, their next opponents in the league, and Bowyer knows a lot is bound to change with a third of the season remaining.
He added: "Whenever you come away and pick up points they're always gained.
"Overall we've got to be more happy than Middlesbrough with the point.
"There are still a lot of teams in it and results can change very quickly. I don't think that anyone's guaranteed anything this season in the Championship."
Boro's Spanish boss Aitor Karanka oversaw a third straight stalemate following fruitless meetings with Wigan and Doncaster and rued his side's lack of killer instinct, while not forgetting to commend Robinson.
He said: "It's frustrating for me today because we didn't play well against Doncaster, and we didn't deserve to win the game against Wigan but today we had a lot of chances.
"We didn't score but that's football and I'm more confident than I was after the last game.
"The keeper did very, very well and today the keeper stopped us so we have to improve with our chances."
Boro are eight points off the top six in 12th place and Karanka shares Bowyer's sense of caution over making end-of-campaign predictions.
"The end of the season is very far from here," he added. "The most important thing is seeing where we are at the end of March, or in April.
"But at this moment that's two months away and we are four games without a win."