Taylor top-scored with 137, and Nicholls was unbeaten on 124 off just 80 balls, lifting the hosts to 364 for four after they lost the toss
With Sri Lanka chasing New Zealand's 319 for seven, they were on the ropes at 128 for seven when Perera opened up.
All-rounder Jimmy Neesham and opener Martin Guptill are also in the Twenty20 squad to face Sri Lanka
In reply to New Zealand's 371 for seven, Sri Lanka were all out for 326 with six balls remaining.
With de Grandhomme out and Corey Anderson injured, Jimmy Neesham and Doug Bracewell have been recalled as all-rounder options
The overwhelming victory gave New Zealand the series 1-0 after the first Test in Wellington was drawn.
At the crease were Dilruwan Perera on 22 and Suranga Lakmal on 16 with their 660-run target out of sight.
Play resumes on the fourth day Saturday with Dinesh Chandimal on 14, Kusal Menis on six and Sri Lanka needing another 636 runs
Shapoor Zadran named in Rashid Khan-led Afghanistan squad
Steve Smith rises to No.2 in Test rankings
Dananjaya, Williamson reported for suspect bowling actions
Vikram Rathour likely to succeed Sanjay Bangar as India's batting coach
Archer's 6-45 scythes through Australia to hand England the advantage
Sri Lanka opt for three short-form games over Tests in Pakistan
PCB announce itinerary for next year's England tour
New cultural charter in works to avoid future scandals
Combined stats of the two 'W's'
Hossain jumps in to defend Jimmy Anderson