England, looking for a series-levelling win after losing the first Test in Kandy last week, took their first innings to 327-7 by lunch on the second day at the Sinhalese Sports Club.
Wicket-keeper Prior was unbeaten at the break on 60, his fourth Test half-century studded with eight boundaries, and left-handed Sidebottom was on 13.
The pair frustrated Sri Lanka for 78 minutes after England, resuming at the overnight score of 258-5, were reduced to 272-7 within the first hour of play.
Australian umpire Daryl Harper, who on Sunday controversially ruled Kevin Pietersen out caught when TV replays showed the fielder may have scooped the ball off the ground, faced a similar situation again on Monday.
Sidebottom fended at a short ball from Dilhara Fernando and Sri Lankan captain Mahela Jayawardene took the ball low at second slip.
Harper consulted his colleague Aleem Dar and then asked TV umpire Gamini Silva to rule if the catch had been taken cleanly.
Slow motion replays, however