Murray, a four-times runner-up at Melbourne Park, likes nothing more than fending off the heavy hitters and had too much craft for Groth as he won the first nine games on the way to a straightforward 6-0 6-4 6-1 victory.
Groth was making his first ever appearance on Rod Laver Arena, and it showed as he was taken to the cleaners.
“He didn’t start the match off serving that well, which helped,” Murray told reporters after his 91-minute victory.
“Because I was returning well, that maybe put some more pressure on him.
“I tend to enjoy playing against that game style. Always did since I was a kid.”
Groth began the match having blasted 27 aces and the fastest serve recorded at the tournament so far at 235 kph in his first round victory against Adrian Mannarino.
Against Murray his first ace did not arrive until the second game of the second set, by which time he was already reeling from a slow start punished by the 28-year-old Scot.
Murray was lobbing and passing at will and such was his complete mastery of his opponent, all Groth could do was shake his head and offer a wry smile.
“I wasn’t making first serves,” Groth said. “Wasn’t making first volleys. He’s too good of a player not to do that against and not a guy you want to get behind against either.”
Groth finally got on the scoreboard in the 10th game, the Australian raising his arms in triumph to earn a massive roar from the parochial crowd.
Murray lost his momentum and Groth broke back as he levelled the set at 4-4.
“I think I held serve, got a game on the board, released a few nerves and probably just started playing the way I wanted to,” Groth said.
Murray, however, regrouped and broke Groth’s serve to seal the set then ran away with the decider to set up a third round clash with Portugal’s Joao Sousa.
Despite his easy progress so far, however, Murray said he felt there was a lot of work to do before his next match.
“There’s some things I certainly could have done better,” Murray said. “I didn’t serve a high percentage of first serves. I wasn’t hitting the ball from the back of the court as well.
“It’s been a very good start but I can still get better.”
(Reporting by Greg Stutchbury; Editing by Amlan Chakraborty/Patrick Johnston)