Teenager Kapugedera finished on 134 not out and Samaraweera was unbeaten on exactly 100 as Sri Lanka made 521 for five declared on the second day of four against Sussex.
Their hundreds, allied to that of inexperienced opener Upul Tharanga (140), helped vindicate Sri Lanka coach Tom Moody's decision to omit recently-arrived veteran left-handed batsman Sanath Jayasuriya from this match after the former captain announced he was ending his Test retirement.
Before stumps Sri Lanka also had the added bonus of taking a wicket with fast bowler Lasith Malinga, who could add firepower to what was a largely innocuous first Test attack after being omitted from the drawn series-opener at Lord's, having Richard Montgomerie caught behind down the legside for 27.
Sussex, as is now the common trait among English counties facing touring teams, were fielding an under-strength side and Sri Lanka, who batted for 14 hours to save the first Test of three, gorged themselves on runs.
They quickly lost skipper Mahela Jayawardene (45) without addition to his overnight score.
But Kapugedera and Samaraweera then established a record partnership for any wicket in matches between the sides by adding an unbroken 238 in 63 overs for the sixth wicket.
Kapugedera, playing in only his eighth first-class game, stroked 11 fours on the way to a maiden century while Samaraweera's patient hundred was his second of the tour.
Jayawardene fell when he was caught behind off James Kirtley, Sussex's acting captain, in what was the pace bowler's first match this season since remodelling his action.
Kapugedera though was undaunted and pulled fast bowler Duncan Spencer to square leg for four.
The 19-year-old later moved into the forties with a superb cover-driven boundary and another through mid-wicket off young off-spinner Ollie Rayner.
Kapugedera reached his hundred in untroubled fashion, courtesy of a pull to the mid-wicket fence off Kirtley, in just under three hours.
Samaraweera got to three figures too but only after being dropped on 98 by wicket-keeper Andrew Hodd standing up to medium-pacer Neil Turk.
In all Kapugedera faced 204 balls with 15 fours.