Chelsea signalled their intent to keep the pressure on title favourites Manchester United by attacking the visitors from the off.
As early as the third minute, Didier Drogba let fly from 30 yards, a fizzing low right-footer which Mark Schwarzer failed to hold. Thankfully for Boro the ball was cleared from danger.
But seconds later came the breakthrough. A left-sided free-kick by Wayne Bridge was met by Carvalho's powerful header as the Portugal international out-jumped the Boro defence to plant the ball wide of the helpless right-hand dive of Schwarzer and into the net.
Drogba almost netted number two on nine minutes, but glanced the ball from Salomon Kalou's corner into the side-netting.
Middlesbrough's first effort on goal came from the right boot of Stewart Downing who forced a low right-handed save by Carlo Cudicini on 14 minutes.
Juliano Belletti was made to clear a 21st minute byline cross by Luke Young as Cudicini misread the flight of the ball.
Two minutes before half-time, Drogba saw his goal-bound free-kick from 25 yards deflected for a corner.
From the resultant corner, the ball was fed back into the penalty area by Belletti and Drogba should have headed home from close range but instead headed over Schwarzer's crossbar.
Sustained pressure by Chelsea in the second half created a series of corners, with the best chance falling in the 49th minute to John Terry who headed powerfully towards goal from ten yards out only for Schwarzer to make a comfortable save.
From another corner on 57 minutes the ball fell to Michael Essien who let fly from the edge of the penalty area, a half-volley which inched over Boro's crossbar.
Both managers decided changes were needed to lift the game, with Chelsea replacing Michael Ballack with Shaun Wright-Phillips on 64 minutes and Middlesbrough bringing on Afonso Alves for Tuncay.
Wright-Phillips could have scored with his first couple of kicks, but the first saw him drive the ball across Schwarzer and miss the far post. Seconds later he skied a sitter from just outside the penalty area with the goal gaping.
Alves had a great chance to equalise with his first effort on goal, but somehow managed to head wide of Cudicini's goal from six yards out.
On 73 minutes Middlesbrough had a wonderful chance to score. A long ball beat the Chelsea rearguard and Alves set off on a run.
Out came Cudicini who completely missed the ball leaving Alves the simple chance to clip the ball home from a wide angle. However, the Brazilian was unfortunate to see the ball zip off the turf and rebound back into play off the post.
The visitors should have scored with eight minutes remaining when first Alves and then David Wheater both hit the Chelsea crossbar before Jeremie Aliadiere blasted the ball over from six yards out.
Chelsea brought on Alex to help out the defence as the home side ran out time to record three vital points.