Busy City striker Jack McNabb was unlucky not to level the scores five minutes later as he watched his first time volley tipped on to, then over, his opponents' cross bar by a desperate Wheeler.
As the half wore on, the home side resorted to firing largely harmless long balls in an attempt to beat the offside trap with little reward, until the visitors, through Warrick Gibson, doubled their advantage from a botched corner after 25 minutes.
The introduction of Joel Hollinshead spurred City into action in the second half, with the noticeable addition of pace unsettling a back division that had looked far more assured in the opening stanza.
Yet, apart from a successful McNabb penalty midway through the second half - swiftly answered by a third Claudelands goal from the boot of impressive two-goal hero Gibson - City were left to regret a slew of half chances and poor touches in front of goal that consigned them to the foot of the Northern Regional Football League Division Two table.
City assistant coach Martin Smith bemoaned his side's lack of composure in front of goal. "We seem to keep the ball well enough, it's just that attacking third," said Smith.
"That's the one thing about this league, if you don't put your chances away you get punished."
Smith praised the work of Hollinshead, whose added zip brought another dimension to the attack in the second half.
"We brought him in today because we knew we were lacking a little bit. "
Claudelands Rovers 3 (Warrick Gibson 2, Darius Kubuya) beat Tga City United 1 (Jack McNabb).