The win moves the club from the United Arab Emirates four points clear of second-placed Tractor from Iran, who drew 0-0 with Uzbekistan's Pakhtakor earlier in the day, with one round of matches remaining.
Only the winners of each of the 10 groups in the newly expanded competition are guaranteed a place in the next phase, where they will be joined by the six runners-up with the best records in the last 16.
Jeferson Collazos had given Air Force the lead 15 minutes into the game but goals from Khaled Ba Wazir and Saleh meant Sharjah led at halftime.
Collazos struck again for the Iraqi club seven minutes after the restart only for Saleh to head home the winner on the hour mark.
In Group D in Riyadh, Xavi Hernandez-coached Al Sadd from Qatar moved within a point of sealing their place in the knockout rounds as South Korea international Nam Tae-hee scored the only goal of their meeting with Iran's Foolad.
Al Sadd top the group by two points from Saudi Arabia's Al Nassr, who were surprise 2-1 losers to tournament debutants Al Wedhat from Jordan.
A draw on Thursday against the Saudi side, who reached the semifinals of last year's competition, would be enough to take Al Sadd into the last 16.
Meanwhile, FC Goa shared the points with Qatar's Al Rayyan as Ali Ferydoon's last-minute goal denied the Group E hosts their first Asian Champions League win.
Jorge Ortiz had given the Indian side the lead in the third minute, and the draw leaves them in third place in the group.
Iranian side Persepolis top the standings and are already certain of a place in the next round despite their 1-0 defeat at the hands of Al Wahda from the UAE earlier in the day.
Matches in the western half of the AFC Champions League are being played in centralised hubs due to the ongoing COVID-19 pandemic, with the group phase to be completed on Friday.
Teams in the east of the continent will hold their group games in June and July, with the knockout rounds scheduled to start in September.