City striker Craig Farrell tested Brazilian keeper Adriano Basso after only 45 seconds with a stinging 25-yard drive from Clayton Donaldson's clever chest-down.
Farrell's perseverance earned his side a free-kick 25 yards out which Farrell took himself but his effort cleared both the defensive wall and the crossbar.
The visitors retained possession well but didn't test the City defence until the 20th minute when Enoch Showunmi headed wide from Phil Jevons' cross. The Robins looked to use McCombe's 6 foot 5 inch frame from a free-kick, but the ball arrived at his feet and the defender scuffed his effort wide.
Steve Bowey struck a sweet 25-yard drive straight at Basso, before York City keeper Tom Evans made an excellent save from Alex Russell 18 yards out.
Careless defending by Darren Craddock gave Craig Woodman a chance 15 yards out but the York defender made amends by blocking the resulting shot.
On the stroke of half-time the Minstermen were desperately unlucky not to go ahead. Emmanuel Panther burst into the area and his goal-bound shot was brilliantly parried by Basso. Martyn Woolford seized on the loose ball but his shot from a tight angle struck the post.
The Robins went ahead on 53 minutes. Jamie McAllister's free-kick into a packed area picked out the towering McCombe and his neat back-header flew over Evans into the net.
As the Minstermen hit back in search of an equaliser the dangerous Donaldson appeared to be bundled over on the edge of the area but nothing was given.
Seconds later McAllister's cynical block on the speedy Woolford earned him a booking and gave York a free-kick which Farrell struck wide of the target. Another foul by the BristolCity defence resulted in a further free-kick which Woolford hit goalwards but straight at keeper Basso.
Craddock burst forward after receiving the ball on halfway but his long-range effort slid wide. 20 minutes from time McCombe almost scored his second when he ghosted in at the near post from a corner but his flicked effort missed the far post by inches.
In a late York rally Donaldson was desperately unlucky to see his shot from the edge of the area pushed round the post by keeper Basso at the end of a superb and incisive break.
Despite the narrow defeat the York players left the pitch to a well-deserved standing ovation.