A solitary goal in the final 10 minutes was enough to ensure a valuable three points in Group B of the Asian Cup
Yu struck in the final 10 minutes with a deflected free kick to give Alain Perrin's side a memorable win.
China dominated the opening half but were unable to take the few chances they created, and they looked like being punished on the hour when Saudi Arabia were awarded a spot kick.
However, Hazazi – who was fouled by Ren Hang – saw a weak effort from 12 yards that was saved by Wang Dalei.
And the striker was left to rue that mistake as Yu grabbed all three points in the opening round of fixtures in Group B.
A positive start from Saudi Arabia saw them threaten the China defence in the opening 10 minutes, however the three-time winners were unable to test goalkeeper Wang.
Having survived the early pressure China grew into the game and had the better of the half with Yu and Ji Xiang leading the charge – the former unable to convert a Zhang Chengdong cross.
Zhang was then presented with a chance of his own three minutes after the half-hour, the 25-year-old receiving the ball on the edge of the penalty area only for a superb block from the Saudi defence.
As half-time approached, China continued to threaten and Wu Xi went agonisingly close to breaking the deadlock.
The midfielder broke from the halfway line having collected a pass from Hao Junmin, before beating one defender and – while holding off two more Saudi challenges – firing a low effort just wide of the left-hand post.
Neither side look like opening the scoring in a scrappy start ot he second half, however that all changed on the hour following a swift Saudi counter-attack.
Hazazi was released in behind the China defence after his side had soaked up some pressure, the striker made good ground into the penalty area before being crudely scythed down by Ren.
The 26-year-old stepped up to take the spot kick himself, but his run-up was too casual and a weak attempt was easily saved by Wang to his left.
Saudi Arabia were punished in the 80th minute as Yu's free kick found the net, deflecting off the defensive wall to take it out of goalkeeper Waleed Abdullah's reach.
China had to deal with late pressure from their opponents in the closing minutes, but Hazazi found himself isolated to hand victory to Perrin's charges, moving them level with Uzbekistan - who they play next - after the first set of games in the pool.