A late Dani Ayala goal proved to be scant consolation as Boro were denied a point on the road at Birmingham City.
Ayala levelled the scores with three minutes to go, but the Blues grabbed a late winner through Odin Bailey to snatch the points from the Teessiders.
Woodgate kept the same starting line-up, and Boro started the contest slowly, allowing Birmingham to get an early foothold in the contest and to dictate the early pace of the game.
Darren Randolph pulled off a fabulous save inside two minutes when he denied Fran Villalba and Alvaro Giminez headed just wide when presented with a good chance.
The Boro goalkeeper had to react well to claw away a free-kick which took a deflection off Dael Fry and he also had to be alert after a Maxime Colin cross was deflected towards goal.
Lee Camp had to be at his best to beat away a piledriver off a free-kick from Marcus Tavernier with Boro’s first teal attack of the game, and Paddy McNair headed the resultant corner wide of the mark.
But the home side did take the lead on 32 minutes, though. A diagonal ball picked out Colin on the right and Villalba made no mistake this time when he drilled the ball beyond Randolph.
And the home side looked for a second. Jude Bellingham had an effort deflected for a corner, and in stoppage time Kristian Pedersen headed against the bar before Jonny Howson headed the rebound off the line.
Woodgate needed another response from his players and while it was the home side who again started the better in the second half, Boro slowly came more into the contest and started to enjoy good spells of pressure.
Camp had to fist away a goalbound cross from McNair and Ashley Fletcher tested the home goalkeeper, but for all the endeavour, Boro failed to find the killer passes in the opposition third of the pitch.
And when Birmingham threatened again, they looked dangerous, Gary Gardner fluffing a great chance to put the game beyond doubt when he struck the upright when Randolph was stranded.
But the equaliser did come and there were just three minutes remaining. Assombalonga dinked the ball into the middle and Ayala powered home from close range to spark wild celebrations in the away end.
After showing great character to battle back, Boro were undone when Bailey headed home the winner for Birmingham just two minutes after Ayala had restored parity.