Australia wrapped up the victory in three days after dismissing the tourists for 148 in the second innings.
Playing his first Test for 18 months, Pattinson ran through the fragile Windies top order to secure his fourth five-wicket haul in Test cricket.
Kraigg Brathwaite was the only visiting batsman to show any resistance at the Bellerive Oval with a patient 94.
Australia take a 1-0 lead in the three-match series, and could return to the top of the ICC Test rankings if they complete a 3-0 series win with victories in Melbourne and Sydney.
Australia captain Steve Smith chose to enforce the follow-on after Josh Hazelwood and Peter Siddle took just five overs to take the West Indies' remaining three first-innings wickets.
There was time for Darren Bravo, 94 not out overnight, to complete his seventh Test century as West Indies posted a first-innings total of 223 in response to Australia's 583-4 declared.
Australia skipper Smith has "no doubt" he will be fit for the second Test in Melbourne starting on 26 December despite suffering discomfort in his knee and hip at Hobart.
Smith will sit out his Big Bash League side Sydney Sixers' domestic fixtures against Sydney Thunder and Hobart Hurricanes after aggravating an injury in his right knee and straining his right hip.
Usman Khawaja could return to the squad after missing the last two Tests with a hamstring injury, but coach Darren Lehmann wants the Sydney Thunder batsman to prove his fitness in the Big Bash first.
"Usman's first got to be fit - if he's not fit he won't play, there's no doubt about that," Lehmann said.
West Indies fast bowler Shannon Gabriel will return home after suffering an ankle injury in the first Test defeat.
Gabriel could not bat in either innings after suffering a stress-related injury to his left ankle late on the opening day on Thursday.
The West Indies have lost seven of their nine Test matches this year, with a win and a draw against England the only positives for Caribbean cricket in 2015.
Amid the loom, Windies legend Brian Lara has suggested that could be tempted by a role on the West Indies coaching team.
Lara, 46, who has been playing festival cricket in Western Australia this week, told former Australia spinner Shane Warne on Twitter that he would be willing to help out coach Phil Simmons and his team.
Lara scored 11,953 Test runs in 131 Tests for the West Indies between 1990 and 2006.
James Pattinson took 5-27 as Australia beat the West Indies by an innings and 212 runs in the first Test in Hobart.