Moments later the Chiefs were in again for their fourth try when Nanai-Williams sparked the attack once more and resulted in the other winger Asaeli Tikoirotuma to run in uncontested and narrow the margin to 37-29.
The Fijian flyer, Tikoirotuma wasn't done as he cashed in for his second try after some brilliant interplay between the backs and forwards in the lead up as the Chiefs stormed right back into the contest.
A pair of Goosen penalties put the Cheetahs out to a seven point lead but then Nanai-Williams jinked his way past the defence to score under the posts after the full time hooter had sounded and Cruden slotted the conversion to even up the scores 43-43.
The Chiefs return home from their three week trip of Australia and South Africa after two successive draws and will prepare to host the Melbourne Rebels at Waikato Stadium.
The match will played next Saturday with kickoff scheduled at 7.35pm.
Chiefs: 43 (Pulu 2, Tikoirotuma 2, Nanai-Williams 2 tries; Cruden pen, 5 con)
Cheetahs: 43 (Pretorius 2, Benjamin, Prinsloo tries; Goosen 5 pen, 4 con)