Stand-in City skipper Nabbout scored the winner in the 49th minute but went down with a right knee injury minutes later after attempting to win the ball against United defender Charbel Shamoon at AAMI Park.
Earlier, on-loan Celtic attacker Tilio was distraught when forced from the field after going down clutching his left hamstring in the 38th minute.
It left coach Aurelio Vidmar counting the cost of City's otherwise impressive response to their derby loss to Melbourne Victory.
"First of all, it was a great win. The boys showed terrific character, and we had really a nice intensity about the game for 90 minutes," Vidmar said.
"But we're all a little bit deflated with the injuries to Tils and to Andy.
"So Tils looks like it's obviously a hamstring and Andy's a knee. We won't know for a couple of days till they get the scans."
Andrew Nabbout's (left) goal gave City the win but his night was soon to turn sour. (Con Chronis/AAP PHOTOS)
Nabbout, 31, has had bad luck with injuries, most recently suffering an achilles problem in 2023.
When asked if there were concerns Nabbout had an ACL injury, Vidmar said: "At this stage it looks like it is, but, we're gonna have to wait till he gets a scan so it's confirmed."
Tilio, 23, was injured when he was breaking through the middle of the park and was knocked off balance in a challenge.
He immediately grabbed his left hamstring when he hit the ground and sank his face into his hands as he limped off the pitch and down the tunnel.
Tilio has had a rotten past two years, suffering multiple hamstring injuries last season after previous quad issues.
Vidmar was unsure whether Tilio's hamstring injury was high-grade.
"Not sure. He said, obviously he felt a spasm in the hamstring," he said.
"Again, I'm no doctor, no physio, so he feels like it's not as bad as it was last year. So, touch wood."
City were already without Max Caputo, Arion Sulemani and Alessandro Lopane through injury - but welcomed back Mathew Leckie in the 78th minute.
Melbourne City's Marco Tilio was forced off with a hamstring injury. (Joel Carrett/AAP PHOTOS)
With captain Aziz Behich suspended, Vidmar turned to Nathaniel Atkinson at left-back, and he impressed in front of Socceroos boss Tony Popovic.
City dominated the first half, but United's Riku Danzaki flashed a late shot into the side netting when he should have squared the ball.
United peppered the City goal in the second half without reward.
Coach John Aloisi was unhappy with the first half but felt United created enough chances to get something out of the game.
"I think we should have got a point," he said.
"We played some really good football, and we created some good openings.
"So it's disappointing we come away with nothing."
Fourth-placed City (2-0-1) will regain midfielder Jimmy Jeggo from suspension for next Sunday's away game against Perth Glory while 10th-placed United (0-2-1) play Adelaide away on Saturday.
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