The Swans, who avoided a third defeat of the season even if they have not won enough games to please manager Graham Potter, made life difficult for Boro despite their impressive record on home soil.
Chances were few and far between at both ends and a point for both sides was probably a fair reflection of a game which did not see either goalkeeper have to make too many saves.
Middlesbrough did threaten a bit late on but in the end manager Tony Pulis had to settle for a draw which lifts them level, albeit second on goal difference, with leaders Leeds in the table.
Middlesbrough's midweek victory over Bolton meant they had won their previous four home fixtures but not even a change of system made them tick properly for long periods.
Stewart Downing's distance drive that had to be turned behind by goalkeeper Erwin Mulder was all the hosts could muster in the opening 20 minutes, however, as Swansea threatened to gain the upper hand.
The Swans, who have had a mixed bag in terms of results so far this season, passed the ball around confidently and looked the more dangerous during that opening spell.
Middlesbrough goalkeeper Darren Randolph had already had to hold an Oli McBurnie header, which he should have done better with, before the Irishman made an instinctive stop at his near post to prevent Martin Olsson from heading in.
That prompted Pulis to scrap his initial approach, switching to a three at the back with wing-backs. It sparked Middlesbrough into life as an attacking force, even if the opener was still not forthcoming.
Midfielder George Saville, who hit his first goal in midweek since moving from Millwall, clipped the bar with a 25-yard strike, while Britt Assombalonga - included ahead of Jordan Hugill - volleyed Jonny Howson's back-post cross at Mulder from a tight angle.
After the restart there was nothing much between the two teams again, with neither goalkeeper tested until after the hour. Before that the closest Middlesbrough came was when Ryan Shotton's excellent delivery was not turned in by either Martin Braithwaite or Assombalonga.
Swansea still saw plenty of the ball in the remaining stages of the game but neither Mulder nor Randolph was asked a serious question, so the goalless draw looked the likeliest result.
Both Pulis and Potter made changes in the closing stages in a bid to get something, but nothing had the desired effect, including a Daniel Ayala header that was held by Mulder.
Pulis said: “Were we as brightly and sparkly? I am not sure. I was last in the Championship working 11 years ago, you look at it now and there are more quality players, playing in better stadiums, the pitches are better, the quality is better, and there are better players who are playing international football.
“And yet we are asked to play eight more games than the Premier League, there’s more Premier League players playing international football, someone has to look at it, to ask players to play Saturday, Tuesday, Saturday ... you look at the top teams, you ask their managers if there’s a little tiredness in there.
“This league has pushed on, it is better in every way shape or form, but to ask them to play eight games extra, it’s a lot of games compared to the Premier League.
“We have had the opportunities and chances again here, you need that spark in the final third to get what we needed. We had the chances in first half and second half, we needed a break.
“Swansea defended ever so well from set plays. When things do go our way in the final third we win games, but when they don’t ... that’s where games are won and lost.
“We needed a break, we needed the one that hit the bar off George Saville. It needed a goal, we played some good football.”