Alexander Zverev double-faulted on a first match point but sent down a winner on his third chance to advance to another semi-final at the ATP Halle event on Friday.
The 22nd-ranked German remains the last home hope on the pre-Wimbledon grass after defeating Nicolas Jarry 7-5, 6-3 in two hours in their quarter-final.
Zverev has twice finished runner-up here and is aiming to go one victory further after not losing a set so far this week.
“I’m unbelievably happy,” the winner said. “I’m glad to be in the semi-finals, there are no easy opponents left.
“I’m also happy to be on the grass again.”
Zverev said that nerves were involved as he won a 16-plus-minute penultimate service game, saving three break points.
He added that serving it out was also a challenge.
“It’s human to get nervous, to not play at the same level for two hours.- it just happens.
“You just deal as best you can and that’s what I did today.”
Zverev was out-hit by his Chilean opponent 25 winners to 19 but came up with a dozen aces in victory.