Jay Bothroyd's third goal of the season - and his second in four games - after 22 minutes had put Wolves on course for a fourth successive win in front of their own fans.
But City centre-half Fontaine ended those hopes when he earned Gary Johnson's side a well-deserved point with a header just five minutes later.
It was no more than City, who had gone into the game on the back of a four-game winning run, deserved.
The Championship new-boys once again proved that their flying start to the season has been no fluke as they posed Wolves a host of problems - particularly at the start of the second half.
But Wolves should have been out of sight by then having squandered a number of excellent first-half chances.
Wolves were rewarded for a spell of pressure when Bothroyd pounced from 18 yards.
Michael Kightly whipped in a corner that caused panic in the City area. Andy Keogh's flick towards goal was punched out by goalkeeper Adriano Basso but his clearance flew straight to Bothroyd who rifled the ball home from the edge of the area.
Stephen Ward and Bothroyd then wasted chances to increase Wolves' advantage and that proved costly when Mick McCarthy's side were caught napping at a set-piece.
City winger Michael McIndoe, who was booed mercilessly by the Wolves fans following his summer switch to Ashton Gate, lifted a free-kick deep into the area.
Fontaine ghosted in unmarked at the far post and easily beat Wayne Hennessey with a close-range header.
It should have been a false dawn for City as Stephen Ward then missed another golden chance two minutes later after Basso had spilled a Kevin Foley cross.
Stephen Ward was just six yards out but hit his weak shot straight at Bradley Orr who cleared off the line.
Wolves were unable to find the same intensity at the start of the second half and had to ride their luck to stay on level terms.
Darren Byfield was inches away from firing City into a 47th minute lead before the hugely impressive Marvin Elliott went close twice.
He forced a full-length save out of Wayne Hennessey from 30 yards in the 53rd minute before firing just over the bar from long range 12 minutes later.
Having successfully ridden that storm, Wolves worked their way back into the game and it needed a fingertip save from Basso to keep out a goalbound header from Darren Ward in the 74th minute.