The 20-time Grand Slam champion served typically smoothly, but Edmund did not let him run away with things in the second set, and saw four break-back points saved.
"We grew up together".
Kecmanovic became the first lucky loser to reach the last eight at Indian Wells since the ATP's Masters 1000 series launched in 1990.
"It will be amusing that somebody other than Novak is still in", he said of his famous countryman.
Kecmanovic, who gained entry to the second round when fifth-seeded Kevin Anderson withdrew with an elbow injury, is in his first ATP quarterfinal.
"He's been around for so many years and he doesn't really get overwhelmed by the occasion of playing on center court", he told reporters.
Roger Federer and Rafa Nadal remained on course for a mouthwatering semi-final clash at the BNP Paribas Open with straightforward fourth-round victories in the California desert on Wednesday. That's especially true after Novak Djokovic and No. 3 seed Alexander Zverev were upset in the other half of the bracket.
"The difference between players is not huge". "Is true that for the last 10 years didn't happen very often".
The Swiss needed less than an hour to see off compatriot Stan Wawrinka in the prior round and the clock had only just ticked beyond the 60-minute mark before Edmund was dispatched 6-1 6-4.
"I hope I can get there", Federer said, "but I'm not going to underestimate Hubert". "He's got everything in the game". But he couldn't overcome Nadal, who lost his serve just once in the 1½-hour match in sunny and windy conditions.
Though Nadal was not fully-satisfied with his performance in the match and said, "I probably played a little bit worse today than yesterday". "Maybe because of the conditions".
His rival in the quarterfinals will be Russian Karen Khachanov who beat American John Isner 6-4 and 7-6 on Wednesday.
The 13 seed will square off against either France's Gael Monfils or Germany's Philipp Kohlschreiber in the quarter-finals on Thursday.
The upsets weren't limited to the men's draw.
A day after world number one Novak Djokovic tumbled out of the third round, 19-year-old Miomir Kecmanovic kept the Serbian flag flying.
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