Karlovic, who fired nine aces to oust first-time ATP semi-finalist Groth after 65 minutes, booked a date in Sunday's grasscourt final against the winner of a later match between Australian Lleyton Hewitt, a runner-up at the event the past two years, and American seventh seed Jack Sock.
Karlovic has not won an ATP title since claiming the fifth of his career last July in Colombia, which ended a win drought of more than five years.
He would jump from 31st to 28th in the ATP rankings by winning the title.
In five career meetings with Hewitt, Karlovic has won four times, most notably eliminating defending champion Hewitt in the first round at Wimbledon in 2003. The Aussie turned the tables by beating Karlovic in the first round at the 2009 French Open.
Karlovic is 2-1 against Sock, having beaten the American last year in the first round at Indian Wells and this year in the Memphis quarter-finals before losing to Sock on Houston clay last April.