The South African world number seven famously beat the 37-year-old at Wimbledon in 2018 over five dramatic sets.
Tiafoe -- who at the age of 20 had already caused the shock of the first round in stunning fifth seed Kevin Anderson -- registered a second notable scalp on his 21st birthday.
Kevin Anderson, a Wimbledon finalist last year, struggled with an elbow injury early in the clash and couldn't cope with Tiafoe's power and finesse.
Tiafoe defeated Gunneswaran 7-6 (9-7) 6-3 6-3 to set up a second-round clash with big South African Kevin Anderson.
With world number five Juan Martin del Potro missing through injury, South Africa's Kevin Anderson is elevated to fifth seed with last year's beaten finalist Marin Cilic at six.
Kevin Anderson had gamely battled for the majority of the 2016 season — a win-loss record of 17-21 portrays its own picture — before the South African decided to stop fooling himself.
Anderson won the first 11 games and needed only 64 minutes to demolish the woeful Nishikori in a remarkably one-sided group stage clash at London's O2 Arena.
The Japanese player joins Novak Djokovic, Rafael Nadal, Roger Federer, Alexander Zverev, Kevin Anderson, Marin Cilic and Dominic Thiem at the elite eight-player event.
The Wimbledon runner-up is expected to be a top draw at the ATP 250 event to be played at the Mhalunge Balewadi Stadium.
Only one change affected the top 10 with Kevin Anderson of South Africa moving from ninth to eighth place while the biggest winner of the week was Georgia's giant-killer Nikoloz Basilashvili.