The Waratahs scored two tries in the first six minutes of the game and their other two in the final seven minutes of the half to lead 31-21 at the break.
In between, they let a 14-0 lead slip and were outscored 21-3 in a 12-minute period to fall behind by four points.
A frantic first half featured seven tries and hardly any scrums, with the first engagement incredibly coming in the 26th minute.
No.8 Dave Dennis capitalised on a fumble from Cheetahs halfback Piet van Zyl to score the first try and lock Sitaleki Timani crossed for the visitors' second after more good work from Dennis.
The Cheetahs retaliated and levelled through converted tries to van Zyl and outstanding winger Willie le Roux.
Halfback Brendan McKibbin kicked a penalty to restore the Waratahs' lead but was the villain soon after when his pass was intercepted by hooker and Cheetahs captain Adriaan Strauss, who ran almost 50 metres to give his team the lead.
NSW scored the last 14 points of the half, with a chip and chase from Adam Ashley-Cooper setting up a try to centre partner Rob Horne and Timani notched his second five-pointer following a slick pass from fullback Bernard Foley.
McKibbin swelled the advantage to 34-21 early in the second half with a penalty, but converted tries to prop WP Nel and le Roux pushed the home team in front.
There was no scoring in the final quarter, though Waratahs five-eighth Berrick Barnes fell just short with a potential match-winning penalty and was preparing for a field goal in the closing seconds, only for his team to turn over the ball after nine phases.
Wallabies winger Drew Mitchell played for almost an hour in his first Super appearance in 13 months, but had little impact.
- AAP
