Fourth-seeded Querrey served 16 aces, to go with the 19 he served in his second round match against Olivier Rochus, to earn a semifinal place opposite second-seeded Philipp Kohlschreiber.
Querrey and Levine, both 25, first played each other as teenagers at a futures tournament in 2006 when Ottawa's Levine was a winner in three sets.
Their careers have since diverged and Querrey has lifted his world ranking to 22 while Levine was forced to qualify in Auckland on his current ranking of 104. Thursday's match was his 10th of the year after he also qualified at last week's Brisbane International.
Top-seeded David Ferrer looked imperious as he downed Slovakia's Lukas Lacko 6-2, 6-1 in only 52 minutes. The Spaniard rebounded after struggling with the pace of the courts in his opening match on Wednesday when he needed three sets and two hours to beat Lu Yen-hsun of Taiwan.
Ferrer will now face the winner of the last quarter-final, due on court later Thursday, between third-seeded Tommy Haas and Gael Monfils.
"No match is easy but I played a very good game, better than yesterday," he said. "I had a good feeling with my game, with my shots and yesterday it was a little surprise for me that the court was faster. But today I felt better."
The win kept Ferrer on target for his fourth singles title in Auckland and his third in as many years, feats that will match those of the great Australian Roy Emerson.
Querrey kept up his drive toward the final with a narrow win over the tenacious Levine. The American won 80 per cent of points on first serve, dropping serve only once in the match — in the third game of the first set.
"The big serve is really helpful, especially in these tiebreakers," Querrey said. "Fortunately I was playing well today. Jesse made it tough today. We've been playing against each other since we were about 13 years old and it's tough every time."
Kohlschreiber reached the Auckland semifinals for the fourth time in nine attempts, posting his 21st singles victory at the tournament at the expense of Belgian veteran Xavier Malisse.