Substitute Matt Derbyshire's second-half goal earned Blackburn a barely deserved point.
David Wheater celebrates Boro's first goal
Defender David Wheater gave Boro an early lead when he headed Stewart Downing's free-kick past Brad Friedel.
Middlesbrough had numerous second-half chances, with Tuncay guilty of an awful miss, while Wheater almost grabbed a second when his header hit the bar.
And against the run of play Derbyshire side-footed into the net from six yards with a quarter of an hour to go.
Boro were ahead on 13 minutes as Wheater claimed his fourth goal of the season when he climbed above Ryan Nelsen to head home a vicious inswinging Downing free-kick.
Blackburn were unhappy the free-kick had been awarded for a foul on George Boateng, but they were left even more unhappy by some poor defending.
Rovers bombarded the Boro penalty box with a series of crosses but goalkeeper Mark Schwarzer was largely untroubled in the first half.
Boro might have doubled their lead ten minutes before the break when an early cross from Gary O'Neil on the right wing caused panic in the Rovers defence.
They need not have worried, however, as Tuncay was unable get a connection.
The home side retaliated through David Bentley, who came close to equalising when his long-range effort breezed past the post.
Blackburn made a less than promising start to the second half as Jeremie Aliadiere was allowed to run into box unchallenged.
But the striker opted to go for goal when a pass to O'Neil would have been the better option.
A minute later and Tuncay needed to only tap Aliadiere's cross into the net but he fluffed his shot.
It was all Middlesbrough and Wheater might have scored his second in the 70th minute, with O'Neil again the provider, but his header hit the crossbar.
Boro were made to pay for their profligacy when Roque Santa Cruz headed the ball into the box and Derbyshire side-footed beyond Schwarzer after Jason Roberts' miscued his shot.
Aliadiere should have sealed victory for Boro in stoppage time but he failed to keep his close-range header on target after a cross from substitute Fabio Rochemback.
Middlesborough defender David Wheater:
"We think we should have won. Tuncay should have put his chance away and we had enough chances to win the game.
"They are a good team but we should have got the three points, really. But we defended well and it is a fantastic point away from home.
"I didn't expect to be playing this season. I thought I would be on loan but I am in the team and scoring goals and it's not going too bad for me."
Blackburn manager Mark Hughes:
"We struggled today. We were a little bit flat. We left ourselves open on the counter attack and they put us on the back foot.
"We were a little but disappointed with the award of the free-kick which led to their first goal but they had a few decisions they weren't happy about either.
"Overall, we are probably happy with the point because they had a number of chances."
Blackburn: Friedel, Ooijer, Samba, Nelsen, Warnock, Bentley, Reid, Dunn (Derbyshire 65), Pedersen (Emerton 65), Santa Cruz, Roberts.
Subs Not Used: Brown, McCarthy, Khizanishvili.
Goals: Derbyshire 75.
Middlesbrough: Schwarzer, Young, Huth, Wheater, Pogatetz, O'Neil, Boateng, Arca (Rochemback 46), Downing, Sanli, Aliadiere.
Subs Not Used: Turnbull, Riggott, Lee, Johnson.
Booked: Boateng, Rochemback, O'Neil.
Goals: Wheater 13.
Ref: Keith Stroud (Hampshire).
BBC Sport Player Rater man of the match: Middlesbrough's David Wheater 8.48 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.