Tim Southee captured the wicket of Edwards' opening partner Kieran Powell (21) and all-rounder Corey Anderson removed first-test double century-maker Darren Bravo (4) but Edwards was a steadying influence, playing powerful and accurate drives off both feet, taking advantage of any width he was allowed.
Anderson removed Edwards by drawing him forward to drive and finding a leading edge which carried to Hamish Rutherford.
Then Trent Boult, the most effective of the New Zealand bowlers, tipped the match in New Zealand's favor by snaring the prized wicket of Chanderpaul.
Earlier, Watling marshalled the highly productive contribution of the New Zealand tail, reaching his sixth half century and giving the big hitters in the lower order a chance to exert their influence.
After the first 75 minutes of the day were lost to rain, he added 38 for the seventh wicket with Tim Southee (21).
Southee and Ish Sodhi (27) fell on consecutive balls but Watling then combined for a 58-run stand the highest ever 10th wicket stand for New Zealand against the West Indies.
"It was good to get a few more runs and get past 400," Watling said. "To take four wickets tonight, the boys are pretty happy and will come back fresh tomorrow to finish it off.
"Our bowlers asked a lot of questions of them. Our lengths were pretty good. It didn't really swing for us, there was a bit of nip but hopefully the wind can change around and give the boys a bit of swing tomorrow."
Tino Best had a chance to become the first West Indies bowler in a decade to take a test hat trick when he removed Sodhi and Wagner with successive balls. Sodhi featured a catch to wicketkeeper Dinesh Ramdin, his third of the innings, and Wagner the only New Zealand batsman who failed to score edged to Darren Sammy at second slip.
Boult faced and defended the hattrick ball, then went on to make 38 from 27 balls with five fours and two sixes.
Sammy, the West Indies captain, continued to use Best in only short bursts. He bowled only two overs with the new ball on Wednesday, after the tourists had won the toss and sent New Zealand in, and he bowled one over at the start of play Thursday, conceding 12 runs, before he was removed from the attack.
He came back strongly to claim the wickets of Sodhi and Wagner and to take some steam out of New Zealand's late bid for runs. But he also dropped a boundary catch off Shillingford which would have ended the New Zealand innings sooner.
Best finished with 4-110 from 21 overs, conceding more than five runs per over, while his new ball partner Shannon Gabriel took 2-86.