At lunch, Sri Lanka were 74 for two with Sangakkara, fresh from his century in the drawn first Test of this two-match series at Lord's, 16 not out and Jayawardene six not out.
With overcast conditions at Headingley traditionally aiding swing bowlers, it was no surprise that England captain Alastair Cook opted to field first after winning the toss under grey skies.
England, on a far more docile pitch, had come within one wicket of victory at Lord's on Monday and Cook clearly had high hopes of his unchanged attack.
But Kaushal Silva fell for 13 when caught behind by Matt Prior off a full-length Anderson delivery.
Also Read
England had a chance to run out Sangakarra for nought after he set off for a single that wasn't on and was sent back.
However, wicketkeeper Prior failed to gather Broad's shy at the stumps from mid-on.
Anderson, after a fine spell of one for 16 in 10 overs, was replaced by fast bowler Liam Plunkett.
On his Yorkshire home ground, Plunkett struck second ball when, from around the wicket, he knocked over left-hander Dimuth Karunaratne's leg-stump with a delivery that swung sharply.