England replied with 49-1 by stumps after losing opener Alastair Cook to the third ball of the innings when he was trapped leg-before by 100-Test veteran Chaminda Vaas.
Captain Michael Vaughan was unbeaten on 13 and Ian Bell was on 36 as England attempt to put up a big score on a barren wicket that is later expected to assist the spin of Muttiah Muralitharan.
The off-spinner, who needs five wickets to overtake retired Australian Shane Warne's world record Test tally of 708, came on in the 12th over and conceded two runs in three overs.
Hoggard grabbed four wickets in a deadly opening burst while Panesar cleaned up the Sri Lankan tail after a defiant sixth-wicket stand of 104 between Kumar Sangakkara and wicket-keeper Prasanna Jayawardene.
Left-handed Sangakkara made 92 and Jayawardene chipped in with 51 to rescue the hosts, who were tottering at 42-5 after electing to bat at the Asgiriya stadium.
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Sangakkara continued the same form that saw him compile 192 in the second Test again