New Zealand had bowled the visitors out in their second innings for 171 about an hour into the day's play at Hagley Oval.
Tom Latham was the only New Zealand wicket to fall before lunch when he failed to handle a bouncer from Mohammad Amir and was caught in the gully by Asad Shafiq for nine.
The victory was New Zealand's first in their last six tests, having drawn the first match with South Africa in August before losing the second then being swept 3-0 by India in October.
"Naturally it's tough coming off a few losses but its good to be home and the boys stepped it up and put some of those feelings of defeat behind us to play a very good test match," Williamson said in a televised interview.
"The first innings it did a bit for both teams and there were two low scores," added Williamson, one of only two players to achieve a half century in the match. Raval scored 55 in his first innings.
"But we knew that second innings would be really important against a strong side like Pakistan who tour very well.
"It was a very good performance."
The visitors had faced an uphill battle to prolong the test, which had the first day washed out, beyond Sunday having resumed on 129 for seven and with a lead of just 62 runs, with only some strong counter-attacking from pace bowler Sohail Khan (40) pushing the target past 100.
"As a professional, as the number two test team in the world we should be better than that," said Pakistan opener Azhar Ali, who stepped in for post-match interviews after captain Misbah-ul-Haq returned home due to a family emergency.
"We should have put in a better batting show, especially the first innings. It was quite helpful for the bowlers but I think we could have scored more runs which would have helped because on that kind of track you're always in the game."
The second test in the two-match series begins in Hamilton on Nov. 25.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
