Nabbout pounced to score via the underside of the crossbar in the 94th minute to earn Aurelio Vidmar's team back-to-back wins after beating Thailand's Buriram United with a late goal in the previous round of league phase fixtures.
"So proud of the team," said City goalkeeper Patrick Beach, who made a string of saves before Nabbout's late goal.
"We dug deep and we believed. We're a very believing group and I'm really happy to help the team and to do my part. Everyone put in a great shift."
City had been gifted the lead by Machida captain Gen Shoji, whose mishit back pass beat goalkeeper Kosei Tani with barely 30 seconds on the clock but Henry Mochizuki levelled the scores with a calm 24th-minute finish.
Machida dominated as the J-League side sought a winner only for Beach to make a series of vital saves to deny the hosts, and Na Sang-ho in particular.
Melbourne City pushed to claim the three points in the dying minutes and those efforts were rewarded when Nabbout pounced after Kavian Rahmani's initial attempt was blocked by Tani.
The win moves Melbourne City up to sixth in the standings on six points, trailing Buriram United on goal difference after Mark Jackson's side defeated Shanghai Port 2-0 in Thailand.
Supachai Chaided put the home side in front in the 15th minute and Curtis Good poked home the second 20 minutes after the interval to leave Kevin Muscat's Shanghai side rooted to the bottom of the eastern league phase with one point.
The top eight finishers in the 12-team table advance to March's knockout rounds with the quarter-finals, semis and final to be played on a centralised basis in Saudi Arabia in April.
Sanfrecce Hiroshima moved up to second with a 1-0 win over Gangwon FC from South Korea with Matsuki Kato netting the winner in the 63rd minute from close range.
The Japanese outfit held on to pick up the points despite playing the final 21 minutes with 10 men following Sho Sasaki's sending off for a second bookable offence.
FC Seoul moved to five points as a 0-0 draw with China's Chengdu Rongcheng saw the South Koreans creep into the top eight.