Both teams had their chances to emerge victorious in south Wales, but they and their relegation rivals had to make do with a point apiece, with Swansea now sitting a point outside of the relegation zone and Boro remaining five points from safety.
After Hull City's 2-1 win over West Ham United on Saturday, Swansea went into the fixture outside of the relegation zone on goal difference but they started brightly as they attempted to return to winning ways.
Their first opportunity fell to Martin Olsson after he had cut inside onto his weaker right foot, but he was only able to hit his shot over the crossbar from an acute angle.
As the first half drew to a close, Swansea's Tom Carroll tried his luck from 25 yards out, only to see his half-volley swerve marginally wide of Valdes's post.
Soon after the restart, Adama Traore did well inside the penalty area before driving the ball wide of the far post, before Lukas Fabianski came out quickly to deny Negredo from close range.
Middlesbrough were showing a greater attacking intent than in the first half, but they almost fell behind when Gylfi Sigurdsson created an opportunity for himself 25 yards from goal before seeing his curling effort parried away by Valdes.
Chances continued to be created in what was turning out to be a much-improved second half, with Alfie Mawson heading wide for Swansea and Negredo slicing wide from eight yards at the other end.
During the closing stages of the game, Swansea pushed men forward in search of a likely winner but to their credit, Middlesbrough remained resolute and dealt with anything which was coming their way.
However, the visitors should have netted a last-gasp winner through Rudy Gestede, who was found by a sublime cross from Negredo, but he headed wide of the target from eight yards out.
Caretaker boss Steve Agnew is likely to be content with a point on their travels, but it was a case of what could have been for the North-West side after they had done superbly to keep their hosts out for the 90 minutes.