Mikael Forssell added a second just before half-time with Gary McSheffrey notching a last minute penalty.
Birmingham, who have themselves been guilty of some sloppy defensive play in recent games, were in no small way assisted to this relegation battle by another poor Boro first-half performance.
After the 3-0 reverse at Bolton there was an obvious need for Birmingham to stage a long overdue improvement, but there were few signs of a turn around of fortunes in the dour opening spell.
Both teams had a desperate air about their play which was hardly surprising in view of the current positions they occupy in the lower reaches.
In this situation a mistake could prove costly and this is how it materialised.
Cameron Jerome's pace took him past two Middlesbrough defenders when Julio Arca took matters into his own hands when he eventually shoulder charged the striker.
He was booked for his pains and from McSheffrey's inswinging free-kick the luckless Downing sliced his intended clearance past his goalkeeper Mark Schwarzer for a deflating own goal in the 23rd minute.
Middlesbrough's goalscoring opportunities were not very frequent. Jeremie Aliadiere produced a powerful drive, but like Tuncay's header just before the break it went straight into the waiting arms of Maik Taylor.
Forssell went close to increasing the lead with a shot which went just wide, but he made no mistake just before half-time when a Seb Larsson corner on the left was headed on by Jerome and his fellow striker bundled the ball home from close range.
Two substitute changes came at the interval, with the introduction Robert Huth and Dong-Gook Lee prompting a Middlesbrough improvement as they were forced to chase the game.
Tuncay, in particular, pulled out all the stops in his bid to get his side back into the game, but the Turkey international was thwarted by a spectacular save from Taylor to keep out a swerving 30-yard drive.
Birmingham then entered their disaster period during the final ten minutes when they have foundered on several occasions this season.
Middlesbrough pounded Birmingham, but this time the Blues managed to survive to produce three much-needed points with McSheffrey converting a last-minute penalty after he had been brought down by Huth.