More than 30,000 fans turned up at the Loftus Versfeld Stadium to watch the game, but they were let down by a below-par City, who ended their tour to South Africa on a low - they lost two and won one match in the Vodacom Challenge tournament.
In the end it was Jeffrey Ntuka's effort minutes before half-time that proved the difference between the two sides.
Former Arsenal striker Adebayor, one of City's biggest summer signings, was handed a first start by Mark Hughes, while another new-boy Gareth Barry also played alongside the likes of Shay Given, Nigel de Jong, Shaun Wright-Phillips and Craig Bellamy.
After a quiet start Martin Petrov and Adebayor both were on the wrong ends of clattering challenges by Chiefs players during the opening 14 minutes, but survived to play on.
But City youngster Javan Vidal, a product of the club's academy, was not so fortunate and was forced off the field after 20 minutes following a collision with Chiefs goalkeeper Itumeleng Khune - Tal Ben-Haim coming on in his place.
Barry had the first real chance for his side after another good cross from the left touchline by the lively Petrov, but his 18-yard shot just short of the half-hour mark was straight at the Chiefs goalkeeper.
The visitors then made another change shortly before the break replacing Richard Dunne with Pablo Zabaleta as the City captain aggravated a knee injury.
In front of goal, all the signs continued to look encouraging with Petrov, Adebayor and Bellamy linking up nicely, until the final ball, which let Hughes' side down.
But it was the visiting goalkeeper Given that was forced to make the first real save, which was in the 41st minute when Nkosinathi Nhleko's shot caused the Republic of Ireland international to dive low to his left and tip the ball wide.
The resulting George Lebese corner caused panic in the penalty area and Ntuka drove the ball home from close-range to hand his side the half-time lead, albeit with a suspicion of handball in his control.
City kept the same players on after the restart with Adebayor's timely run 10 minutes in almost paying dividends, but, after seeing his initial cross-goal pass come back into his path, the Togo striker blazed over when he should have hit the target.
Three minutes later, newly-married Robinho was thrown on for Petrov, but he too failed to inspire the Eastlands club with even half chances proving few and far between.
With 25 minutes to play, a head injury brought Nedum Onuoha's game to an end - Vladimir Weiss coming on in his place.
And the Slovak winger almost helped his side snatch a late goal when his mazy run down the right saw him feed the ball to Robinho, who somehow dragged his shot wide as the game ended disappointingly for the visitors.