New Zealand's batsmen capitalised on a record-breaking bowling spell by Trent Boult on Wednesday to wrest full control of the second Test from Sri Lanka at the end of the second day.
At the close, New Zealand were 231 for two, holding a commanding 305-run lead in their second innings with eight wickets in hand.
Sri Lanka's hopes of taking the series-deciding Test were severely dented in a 15-ball masterclass of swing bowling from Boult when he took six wickets for four runs.
It gave New Zealand a 74-run first-innings lead, which Latham and Raval extended to 195 with a century opening stand.
Kane Williamson and Latham added a further 68 for the second wicket until Williamson played a lazy shot to Lahiru Kumara and was caught at first slip for 48.
At stumps, Latham was on 74 with Ross Taylor on 25.
Latham, who starred in the first Test with an unbeaten double century, has faced 213 deliveries.
He received a life on 32 when he top-edged Suranga Lakmal to fine leg where the ball slipped through the fingers of a diving Dushmantha Chameera.
Patel, who worked with Latham to produce the first wicketless session in the Test when they batted from lunch to tea, was out in the second over after the resumption for 74 when he edged Dilruwan Perera to Kusal Mendis at short leg.
Earlier, New Zealand was able to build on a wholly unexpected 74-run first innings lead, achieved when Boult took six wickets for four runs in the space of 15 balls to send Sri Lanka tumbling from 96-4 to 104 all out.
His first five wickets came faster than any other bowler in Test history; from 11 balls, beating Jacques Kallis's record of 12 balls against Bangladesh in 2002.
Sri Lanka had looked in a strong position when it resumed at 88-4 in reply to New Zealand's first innings of 178 but Boult's test-best return of 6-30 turned the match on its head.
The left-armer, who has 224 wickets in 58 tests, began the day with 0-20 in Sri Lanka's first innings after struggling for form in the first Test at Wellington where he took 2-145. He also managed only seven wickets for 262 runs in three Tests against Pakistan in the United Arab Emirates.
Suddenly the dry spell of wickets turned into a flood and Boult went from 0-26 to 6-30, narrowly missing a hat trick when he took three wickets with four balls.
Boult's first two wickets were caught by his new ball partner Tim Southee in the slips and his next four fell lbw, three within the space of four balls. England umpire Michael Gough gave five decisions in a row in Boult's favor.
His first victim was the overnight batsman Roshen Silva who fell for 21 in the fifth over of the morning, caught by Southee at third slip after driving at a ball which swung late.
Wicketkeeper Niroshan Dickwella fell next to a brilliant catch by Southee, at full stretch, from a ball which also enticed the drive but left him late.
The next four wickets fell at an even more frantic pace and to similar lbw decisions.
Dilruwan Perera shouldered arms at a ball from Boult which was full and swung back onto middle stump.
Suranga Lakmal received a similar delivery from the very next ball and was hit on the toe in front of middle.
Boult had to wait until the next over to chase his hat trick, bowling to the tailender Dushmantha Chameera. Chameera met the hat trick ball with a solid forward defensive shot but was out lbw to the next ball, giving Boult three wickets in four balls and his seventh five-wicket bag in tests.
Lahiru Kumara was his final victim four balls later, also out lbw without offering a shot. Angelo Mathews, almost immoveable in the first test where he scored 83 and 121 not out, was left unbeaten on 33.