Everton started the first half with purpose and strength and could have been 2-0 up within five minutes.
Centre-back Alan Stubbs, up for a corner in the first minute, only managed to sky a free header from two feet out high over the bar.
Four minutes later Stubbs again headed wide from an identical Gary Naysmith corner as Sunderland failed to cope with a barrage of crosses.
Another good cross from Alessandro Pistone in the 27th minute found a towering Steve Watson who crashed a powerful header against the bar.
Sunderland were struggling to have any say in the running of the game but in the 34th minute they scored with their first purposeful attack.
Against the run of play an inch-perfect pass from Kevin Phillips found Kevin Kilbane running into the penalty box and he drilled a low shot past Thomas Sorensen.
Everton eventually got the equaliser early in the second half as US international striker McBride bagged his first goal at Goodison Park.
Scot Gemmill chipped a cross from the right which McBride met with a bicycle kick which took a wicked deflection before hitting the net in the 51st minute.
Everton pressed for a second and should have got it in the 55th minute as Tomasz Radzinski scuffed a woeful volley past the post from four yards out.
But in the 57th minute a good period of Everton pressure was rewarded after McBride finished superbly for his second goal of the game.
The ball came to him on the edge of the box where he miscontrolled, almost fell over, but recovered to hit a snapshot past a static Sorensen.
Black Cats right-back Darren Williams fired a right-footed drive from 20 yards out which keeper Richard Wright parried well as Sunderland desperately looked for an equaliser.
But The Toffees hung on to take the three points and heaped more pressure on to troubled visiting boss Howard Wilkinson.