England, after losing the toss, were 98 for three at lunch in their first Test since suffering a 281-run defeat by Australia in Sydney that condemned them to a 5-0 Ashes series loss in January.
Pradeep had done the bulk of the damage with two wickets for 35 runs in nine overs.
England were left looking to Ian Bell to dig them out of a hole, with the experienced batsman 41 not out in his 99th Test. Joe Root was unbeaten on six.
Mathews's decision yielded a quick reward as England lost both their openers inside the first half hour.
Australia-born Sam Robson, one of three debutants in the England side and playing on his Middlesex home ground, fell for one when he was drawn forward by a full-length Pradeep delivery that took the outside edge and wicketkeeper Prasanna Jayawardene, diving to his right, held a fine catch.
And 14 for one became 22 for two when England captain Alastair Cook exited for 17, the left-hander bottom-edging an intended cut off Nuwan Kulasekara into his stumps.
Bell demonstrated his class by easing first-change Shaminda Eranga through the covers for four with a textbook drive.
And the Warwickshire batsman also dealt well with Mathews, Sri Lanka's fourth seamer, by cover-driving and straight driving the all-rounder for elegant boundaries.
Ballance looked less assured but the Zimbabwe-born left-hander brought up a fifty stand with Bell when he clipped Pradeep off his pads for four.
However, Ballance's 73-minute innings ended when, to Pradeep's fifth ball back, he drove flat-footedly and was caught behind for 23 to leave England 74 for three.
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