Broad appeared to relish the responsibility of being the senior man in the attack in the absence of fellow veteran Jimmy Anderson.
He had figures of 2-20 off nine overs at lunch and could have had a third wicket near the end of the first session, only for wicketkeeper Ben Foakes to put down a difficult catch from an inside edge off Devon Conway.
Conway was 12 not out, having been joined in the middle by Henry Nicholls, unbeaten on one.
Trailing 2-0 in the three-match series, New Zealand won the toss and opted to bat under a blue sky in their bid for a consolation victory but lost Latham for a duck on the sixth ball of the match, with Joe Root taking a catch off Broad at slip.
That brought Williamson, who missed the second Test after contracting the coronavirus, to the crease and he took time to get settled in the face with the ball moving about.
Will Young was the next to go for 20 when he played a forward defensive to the first ball of offspinner Jack Leach's spell and got his bat trapped behind his pad.
It was plumb lbw, as revealed by replays after Young decided to review - perhaps thinking he heard an edge off the bat when in fact it was the bat hitting the pad.
Fast bowler Jamie Overton was pacey, if not so accurate, on his debut and he was briefly joined on the field by twin brother Craig, who wasn't in the team but acted as a sub fielder when Jonny Bairstow went off for an over or two.
Williamson was out for 21, a ball after being surprised by an inswinger from Broad. The next delivery nipped away slightly off the seam and enticed an edge behind to Foakes.
Matt Henry, a fast bowler, dropped out to accommodate Williamson, while Neil Wagner replaced the injured Kyle Jamieson in New Zealand's bowling attack.
