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The left-arm spinner, who has scored 3,329 runs, claimed his 300th wicket when he dismissed his Sri Lankan counterpart Kumar Sangakkara in the afternoon session of the first day's play.
Sangakkara, former captain Mahela Jayawardene and Thilan Samaraweera scored half-centuries as Sri Lanka went to stumps at 262-3 on a firm wicket that Vettori said "looked like a road" at the toss.
Jayawardene was unbeaten on 79 and Samaraweera was on 78, having shared a fourth-wicket stand of 147 after tight bowling by the Black Caps had kept the Sri Lankans on a tight leash.
When play began 30 minutes late due to a wet outfield, Sri Lanka plodded to 146-3 by tea before Jayawardene and Samaraweera caned the second new ball in the final session to boost the total.
Vettori, 30, joined a select band of all-rounders that includes Kapil Dev of India, Ian Botham of England, Richard Hadlee of New Zealand, Imran Khan of Pakistan, Shane Warne of Australia, Shaun Pollock of South Africa and Sri Lankan Chaminda Vaas.
Vettori is already the most successful left-arm spinner in history, having surpassed Englishman Derek Underwood's tally of 297 wickets in the first Test in Galle last week.
Vettori, who began the match with 298 wickets, had left-handed opener Tharanga Paranavitana (19) edging his second delivery to Ross Taylor in the slips.
Sri Lanka suffered a crucial blow in the third over after lunch when Tillakaratne Dilshan, who hit 92 and 123 not out in the first Test, was dismissed for a unusually lacklustre 29.
Seamer Iain O'Brien, who had dropped a return catch off the previous delivery, made no mistake second time as Dilshan mis-timed a drive and looped the ball back to the bowler.
Sangakkara and Jayawardene had put on 40 for the third wicket when Vettori was rewarded a second time during an unchanged 17-over spell to reach the milestone.
Sangakkara, who made 50, pulled a short ball to mid-wicket where Jacob Oram took the catch and ran to his team-mates to join in the celebrations for their captain.
Vettori claimed the second new ball as soon as it was due after 80 overs and himself bowled the first over with it, before handing it to his two main seam bowlers.
Sri Lanka made three changes from the team that won the first Test in Galle, leaving out all-rounder Angelo Mathews, spinner Ajantha Mendis and seamer Nuwan Kulasekara.
They were replaced by batsman Chamara Kapugedera, seamer Dammika Prasad and left-arm spinner Rangana Herath.