The sixth-seeded Australian won six consecutive points in the breaker after falling behind 1-0, closing out Monday's (Tuesday AEDT) match with a forehand winner after struggling with that stroke throughout the match.
Purcell had two match points with a 5-4 lead in the final set when Krueger started a run of nine consecutive points that gave the American wildcard a chance to win the contest by breaking the Sydneysider's serve.
The current world No.43 recovered and forced the tiebreaker by winning four consecutive points. Krueger saved two more match points before losing in a deciding set for the fifth consecutive time.
Purcell will face either Marcos Giron or fellow American Nicolas Moreno De Alboran in the last 16.
Taro Daniel of Japan won the day's other round-of-32 match, 4-6 6-4 5-0 over Constant Lestienne when he retired with an arm injury.
It's the 14th time the 31-year-old Frenchman has ended a match that way.
Daniel won the final seven games against Lestienne, with his opponent taking a medical break before the third set and later getting more treatment.
Daniel and Lestienne broke each other for the first five games of the match before Lestienne held serve and kept that advantage for the rest of the opening set.
Daniel went up 3-0 in the second set before Lestienne levelled at 4-4. Daniel broke Lestienne to win the set, one of a combined for 10 service breaks in the match.
Second-seeded American Tommy Paul is next up for Daniel in the round of 16.
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