Hewitt overcame Roger Federer in the final of the ATP 250 hard-court event last year, but his challenge came to an abrupt halt this time around as Groth put in an assured performance.
Groth secured an early break against his fellow Australian to take a 3-0 lead, and he remained relatively untroubled until serving for the set at 5-3.
Hewitt forced two break points, but Groth was able to rescue those and duly took the lead.
The second set was even more comfortable, as breaks in games one and five secured Groth's passage to the next round, while defeat for Hewitt denies him the chance of a fourth crown in Brisbane.
Groth will now face qualifier Lukasz Kubot, who stunned fifth seed Kevin Anderson with a 7-6 (7-3) 6-4 victory.
Ranked number 177 in the world, few would have given Kubot a chance against South Africa's Anderson, but he recovered from a shaky start to surprise his opponent on Tuesday.
World number 16 Anderson got off to an ideal start with a break in the very first game, but he was left to rue four missed set points at 5-4.
Kubot recovered from 40-0 down in that game to eventually break and force a tie-breaker, which he took in relative comfort.
This time it was Kubot's turn to start with a break of serve in the second set, but that advantage was short-lived as Anderson responded in kind in the very next game.
But Kubot was not to be deterred, and made the crucial breakthrough in game nine before holding his nerve and securing a surprise victory.
Anderson was the only seed to fall on Tuesday, with 2012 runner-up Alexandr Dolgopolov overcoming Carlos Berlocq 6-2 6-3.
The seventh seed will now take on Martin Klizan, who came from behind to see off Jurgen Melzer 6-7 (7-5) 7-6 (8-6) 6-1.
Australian John Millman will have the chance to spring a shock in front of his home crowd when he takes on top seed Roger Federer after defeating Rhyne Williams 6-3 6-1, while Mikhail Kukushkin booked a date with Milos Raonic thanks to his 6-4 4-6 6-4 success over Marius Copil.
Elsewhere, 2008 runner-up Jarkko Nieminen saw off Denis Kudla 4-6 6-1 6-4 and Steve Johnson also came from a set down, getting the better of Marinko Matosevic 2-6 7-6 (7-0) 7-5.
