Fritz, ranked 50 in the world, had earlier dismissed top seed John Isner 7-6 (3), 7-6 (5). "I knew I could", said Fritz.
Top seed and two-time champion John Isner is out of the ASB Classic tennis tournament after his first match.
The big American pulled the break back instantly with a forehand victor at the net after a well-constructed attack, with both players serving well in the remaining six games to set up a tie break where Taylor forged the lead with a mini-break in the very first point.
The 33-year-old saved a match point at 4-6 with a massive second serve, but Fritz sealed the result on the next point, after a Isner backhand drifted over the baseline after the longest rally of the match.
"We had a lot of close points".More news: Missing Wisconsin 13-year-old Jayme Closs found alive
The second set went to a tiebreak without a service break, with Fritz saving the only break point of the set in the third game.
The second set was an even tighter affair - with neither player managing a break - before Isner held a strong game at 6-6.
Fritz gained a mini break at 4-1, before two consecutive aces brought Isner back into contention at 4-4.
Taylor grabbed the first advantage after a short backhand cross court victor in the third point but Isner pulled it back with a strong forehand attack in the eighth point for a 4-4.
Fritz won more tiebreaks in 2018 than any other player and he put that ability to good use Wednesday to claim his fourth win over a top-20 player. "I like to think that one of the strengths of my game is playing under pressure and playing the big moments well".More news: Arsenal midfielder Aaron Ramsey agrees to join Juventus in £36m deal
"So, I'm happy to start every year and today as well playing well under pressure and handling those big moments well".
The four-time ASB Classic champion and a former world no. 3 David Ferrer has played his last match in Auckland, retiring against the 4th seed and compatriot Pablo Carreno Busta already in the middle of the third game due to a right calf injury.
"More often than not, the matches I lose, that's where I get let down".
New Zealander Rubin Statham was beaten in straight sets by Jan-Lennard Struff of Germany, while New Zealand-born Cameron Norrie of Great Britain won his second round match against Joao Sousa of Portugal in straight sets.
After receiving medical attention, he returned to the court to play one more point before withdrawing.More news: Michael Cohen to testify before House Oversight Committee