He then caught captain Kane Williamson for 22 off Anderson and left New Zealand five wickets down with 36 runs on the board and in desperate straits.
New Zealand will resume at 192-6, still 115 runs shy of England's 307.
He was out seven balls later to end the innings.
England still have their noses in front, but New Zealand can thank Watling and de Grandhomme for lifting them back into the contest.
But they grafted and grafted some more, batting 50.1 overs and surviving nearly everything the desperate tourists could throw at them, including a barrage of short stuff from right-arm quick Mark Wood which resembled a Neil Wagner peppering.
In response, Broad and Anderson delivered early with accurate spells to leave the Black Caps reeling.
De Grandhomme was out shortly before stumps when he gave wicketkeeper Jonny Bairstow a fourth catch of the innings off Broad, for 72.
England then got the new ball to swing and seam, with Anderson's delivery to dismiss Watling swinging in, pitching on middle and then seaming into the off stump. He might add New Zealand to the list in the next few days.
New Zealand batsman BJ Watling was at his plucky best against England on Saturday.
Broad back to his best for England
The tourists accelerated to 8-290 by stumps after being sent in, boosted by some lusty late hitting from Bairstow (97 not out) and Mark Wood (52).
Broad added to his tally with the wickets of New Zealand's senior batsman Ross Taylor, caught by Alastair Cook at first slip for two, and Henry Nicholls was out on review to an lbw shout without scoring.
He and Raval could be excused for losing their wickets to quality bowling.
Christchurch-born all-rounder Ben Stokes and Bairstow led the recovery, putting on 57 for sixth wicket but England's fortunes nose-dived again when they lost Stokes (25) and Stuart Broad (5) at the start of the final session.
England's Jonny Bairstow celebrates his 100.
Tim Southee and Trent Boult engineered another England meltdown today to have the tourists 150 for five at tea on day one of the second Test here.
Leach was the first man out this morning, caught by Watling from the bowling of Tim Southee who finished with 6-62.
England pace bowler Stuart Broad carved through New Zealand's batting line-up with a superb four-wicket haul to help put his side in an advantageous position on the second day of the second Test in Christchurch.
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