The British number two fought back from a set down and then recovered from 4-2 down in the deciding set against his Serbian opponent to leave himself serving for the match at 5-4.
Evans was 40-0 up and held three further match points in the same game but was unable to take any of them as Kecmanovic, who saved one chance with a between-the-legs shot, broke back.
The Serbian then had his own chance at 6-5, which Evans saved, only for Kecmanovic to win the final four points of the tie-break in a 6-3 3-6 7-6 (4) success.
"That was the first time that I was able to do that," said Kecmanovic, who is ranked eight places below Evans at 33.
"I was completely tuned out of the match and I just went for it in that moment."
Nick Kyrgios fought back from a set down to defeat Kamil Majchrzak 3-6 6-2 6-2 and reach the quarter-finals while fourth seed Frances Tiafoe was a 6-1 7-6 (7) winner over Bernabe Zapata Miralles.
Kyrgios won his third ATP Tour title at this event as a 21-year-old in 2016 and said he always loves coming back to Japan.
"It's always a part of the season and a tournament that I always play, because I genuinely love being here," he said.
"I love the food, I love the culture, I love the people," added the Australian, who also revealed his love for "anime and Pokemon".
"I still usually travel with my Nintendo Switch all the time, playing all these games… Things like Pokémon and stuff, that's been my childhood, every day."