Taylor also regained sole grip of the second-most test centuries title from captain Kane Williamson. Taylor has 14, Martin Crowe leads with 17. Watling reached his sixth test century.
Both employed the square cut and pull with authority, and otherwise played Sudoku-like innings plugging the gaps as New Zealand exerted their dominance.
They were parted five overs after the tea break when Watling pulled a short delivery to deep square-leg. The dismissal led Williamson to declare with a lead of 412.
Curiously, and in contrast to the Brendon McCullum captaincy era, there were no sixes in the New Zealand innings.
Boult's wickets in the second and fourth overs had Zimbabwe 17 for four. An unbeaten 49 from Craig Ervine helped them recover.
"Kane told us to just be positive and bat with intent," Taylor said. "You still have to respect the bowlers. We could have batted on longer but it was a good sign to declare when he did."
The New Zealand bowlers took up the baton of domination. Tim Southee had Hamilton Masakadza caught at slip in the first over before Boult bowled Brian Chari in his first over, then dismissed Chamu Chibhabha and Prince Masvaure with consecutive deliveries in his second.
Ervine and Sikandar Raza counterattacked with 69 for the fifth wicket in nine overs. Neil Wagner dismissed Raza for 37 with a short ball.
The Zimbabweans faced an innings defeat, as the effects of not playing a test since November 2014 became clear.
"In the second innings, the guys got some good balls," Masakadza said. "The first innings was poor, a lot of soft dismissals, and that's why we are in the position we are in."
Claims will no doubt emerge that the hosts are unworthy of test status.
However, not so long ago, notably in the era when former captain Daniel Vettori was rumoured to be driving the team bus literally as well as figuratively, the Black Caps suffered similar circumstances. There's also the ghost of 26 to consider from 1955 against England at Eden Park.
Historical suggestions that New Zealand didn't deserve to participate in the longest form were generally admonished.
If the International Cricket Council invests profits from sponsorship and world tournaments wisely and directly, as they have done with development programmes and tournaments for associate members, Zimbabwe could be saved.
That includes actually playing more tests. The hiatus of 20 months between this one and their last in Bangladesh is unacceptable if the ICC's genuine about keeping them in the mix.
The proposal of a two-tier system with promotion, relegation, a more even-handed financial distribution and genuine fairness over who plays where and for how long would be a welcome addition to the test landscape.
Four day tests could also help, given how Twenty20 has advanced the speed of the game in recent years.
Yes, the Zimbabwean era involving Heath Streak, the Flower brothers, Andy and Grant, and Ray Price seems some distance from the current crop but, provided the security situation remains relatively safe, that's no reason to give up on them. Look how investment in the likes of Afghanistan is delivering wonders.
Only Donald Tiripano had played a solitary test from a Zimbabwean pace bowling attack which includes debutants Prince Masvaure and Michael Chinouya.
In the opening session of the third day they dibbled, dobbled, wibbled and wobbled to the crease at around 120km/h like a swarm of Nathan Astles.
Zimbabwe captain and leg spinner Graeme Cremer looked the most potent as wear and tear on the pitch created purchase, in sync with the diminishing bounce. When Cremer pitched on middle and leg he asked questions.
That bodes well for Mitchell Santner and Ish Sodhi today, despite 17 of the 21 wickets falling to pace rather than spin so far.
- additional reporting AFP
