Fast bowler Plunkett, on his Yorkshire home ground, took five for 64 in only his second Test in seven years after he was recalled for the drawn first match of this two-Test series at Lord's.
Broad, who previously took a hat-trick against India at Trent Bridge in 2011, became the first England bowler, and only the fourth in all, to perform the feat twice in Tests after Australia's Hugh Trumble, Jimmy Matthews and Pakistan's Wasim Akram, when he removed Kumar Sangakkara (79), Dinesh Chandimal (45) and Shaminda Eranga with successive deliveries split across two overs.
"To pick up five is a great feeling," Plunkett told Sky Sports.
"My mum and dad were here too, just back from holiday in Cyprus. We created so many chances and beat the bat a lot," the former Durham paceman added.
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England, who had seen Cook win the toss and opt to field first in overcast conditions were clearly confident of inflicting a fresh collapse upon Sri Lanka having come within one wicket of victory after dismissing nine of the tourists' batsmen on the last day at Lord's.
Sangakkara's innings was his third score in excess of 50 in this series, after he made 147 and 61 in at Lord's, and also the sixth successive Test innings in all that he'd past the half-century landmark.
The left-hander could have been run out on nought and was then caught behind on 16, only for neither bowler Plunkett nor wicketkeeper Matt Prior to appeal.
He was given a further life on 27 when Prior dropped a routine catch, again off Plunkett, and missed again on 57, when Moeen Ali failed to hold a far tougher chance at backward point.