Hadlee, regarded New Zealand's greatest cricketer, congratulated Taylor on the achievement.
Taylor is only two days away from becoming the first cricketer to play 100 games across formats.
The 35-year-old will become the first cricketer in the world to complete 100 games across three international formats when he steps out for the first Test against India at Basin Reserve.
Only Stephen Fleming, Brendon McCullum and Daniel Vettori has played more Tests than Taylor who will only enter an elite club by playing his 100th Test in the series opener, beginning in Wellington.
Chasing 274 for a win, Ravindra Jadeja top-scored with a 73-ball 55 while Shreyas Iyer made 52 from 57 balls.
Earlier, Shreyas Iyer hit his maiden century while KL Rahul and skipper Virat Kohli carried on their fine form as India dished out a clinical batting effort to post 347 for four.
Pakistan's Shoaib Malik and India's Rohit Sharma are the only two players ahead of the 35-year-old.
Taylor is now the leading run-scorer for Kiwis on the fourth day of the third Test against Australia at the Sydney Cricket Ground.
Paine summarised that maybe Taylor knows the person who is in charge of dealing with ball-tracking, and was heard saying 'maybe, he knows the bloke'.
Australia were all out for 416 earlier in the day and Mitchell Starc started the rampage with the wicket of Tom Latham in the very first over of the innings.
Taylor reached 7000 runs in just 169th innings, and with this feat, he has surpassed New Zealand's Stephen Fleming who had scored these runs in 189 innings.
New Zealand rode on a 200-run stand between Latham and Taylor to register a six-wicket victory and take a 1-0 lead.