England ripped through the Sri Lankan lower order to bowl the tourists out for 257 and close day one of the second Test at Headingley 221 runs behind.
The Lions were recovering well from 108-4, with Kumar Sangakkara sharing fifty partnerships with Angelo Mathews and Dinesh Chandimal, but four wickets in nine balls for one run saw them collapse to 229-9.
The 36-year-old was snaffled well at gully by Ian Bell, playing in his 100th Test, for 79 to become the first of Broad's victims, and the paceman had Chandimal (45) and Shaminda Eranga caught behind to complete the hat-trick and become the first Englishman to take two in Test matches.
In between Broad overs, Plunkett, who had earlier dismissed Mahela Jayawardene and Lahiru Thirimanne in successive balls and broke a decent opening stand by bowling Dimuth Karunaratne for 28, forced Dhammika Prasad to fend one to Matt Prior.
England had one hour to survive in the evening session, and Cook had an early reprieve when his edge fell just short of Sangakkara, but the home skipper and Sam Robson safely made it to stumps at 36-0.