It looked as if the left-handed opener might bat through the whole of an extended morning session after bad light cut short Saturday's play.
But instead he fell for 55 when caught behind gloving fast bowler Olly Stone down the legside, with Sri Lanka 136-4 at lunch on the fourth day.
That left the tourists, already 1-0 down in this three-match contest after a five-wicket defeat in the first Test at Old Trafford, needing a further 347 runs in pursuit of what would be a record-breaking total of 483.
The highest winning fourth-innings score in 147 years of Test history is the West Indies' 418-7 against Australia at St John's in 2002/03, with the equivalent Lord's record the West Indies' 344-1 against England in 1984.
That Sri Lanka were in dire straits owed much to Joe Root, whose 103 on Saturday, his second hundred of this match, meant the star batsman set a new England record of 34 Test centuries.
Root also held two slip chances before Saturday's close as he became just the fourth outfielder with 200 Test catches to his credit.
But early on Sunday, Root reprieved Karunaratne, who had added just two runs to his overnight 23, failing to hold a fast-travelling one-handed chance from an edged cut off paceman Gus Atkinson.
England did manage an early breakthrough on a sunny morning when Prabath Jayasuriya drove at Chris Woakes, with Harry Brook holding a fine catch at second slip.
It was the end of the nightwatchman's gutsy 41-ball stay, with Sri Lanka now 60-3.
The 36-year-old Karunaratne drove and pulled Atkinson for fours off successive deliveries on his way to a 98-ball fifty including seven fours.
The injury-plagued Stone, in for the sidelined Mark Wood for a first Test for three years, produced a rising 87 mph (140 kmh) delivery that Karunaratne could only flick to wicketkeeper Jamie Smith.
Sri Lanka's hopes at lunch rested with the experienced pair of Angelo Mathews (34 not out) and Dinesh Chandimal (15 not out).
