Australian underdog John Millman firmly believes he’s on the cusp of snaring a big grand slam scalp following a first-round French Open exit which John Isner admitted was a lucky escape.

The American 15th seed described securing the crucial second set late on Monday night, before bad light stopped play, as the equivalent of “pulling a rabbit out of a hat completely”.

An outsider to start the match, Millman was on the verge of taking a two-set lead into Tuesday but squandered three set points on serve when up 5-4 with the darkness gathering.

The affable 26-year-old had further opportunities in a tense tiebreak but again couldn’t deliver the knockout blow and it was left to Isner – and his booming serve – to take the set and the momentum into day three.

On resumption, Isner did enough to hold Millman at bay – prevailing 6-7 (4-7) 7-6 (14-12) 7-6 (9-7) 7-5 – but the Australian had no regrets stemming from the defeat.

“It’s one of those games where you just have a couple of little half chances against someone like John, and sometimes they go your way and sometimes they don’t,” Millman said.

“It’s always going to be a tough match, you’re always going to have your back against the wall against these guys.

“I gave it my all and I was disappointed but I’m glad about the effort I put in.

“… I feel as if you’ve looked at my results over the year, I have been matching it with these guys at this level.

“And I think that’s a good indication moving forward that that’s my level and that’s where I’m at.

“Hopefully I can knock off one of these big guys pretty soon.”

Millman didn’t feel deflated when the match was called for bad light late on Monday, and said there was still confidence within his camp that victory was within reach.

But Isner left no doubt as to how much taking the second set meant to his chances of winning.

“Second set I pulled a rabbit out of my hat completely,” he said.

“He was serving at 5-4, 40-Love to go up two sets to love.

“I was in a world of trouble right there; was able to come back and win in this long tiebreaker, and then it was dark.

“So I definitely slept much better being at one-all than 0-2.

“Then I came out of the gate today and played a really good game and gave it back; had to win another tiebreaker. It was a tough match.”