Broad and Bresnan were quickly back into the groove as they grabbed four wickets apiece.
Broad had been allowed a break following the tour of New Zealand, while Bresnan was back in championship ranks for the first time since he underwent elbow surgery.
The Yorkshire right-armer took a wicket with his first ball on his way to figures of four for 41 as Durham were dismissed for 237 at Chester-le-Street.
Only Phil Mustard's 70 helped the hosts to a batting bonus point before another England candidate, Graham Onions, made early inroads into Yorkshire's batting before stumps. Onions removed opener Adam Lyth for a duck and then ran out Phil Jaques before he had scored.
England batsman Joe Root (30 not out) steadied the ship for Yorkshire, but Onions struck just before the close trapping Andrew Gale lbw, to leave the visitors 57 for three.
Broad ensured Nottinghamshire took control against newly-promoted Derbyshire with figures of four for 57 from 22 overs.
Derbyshire limped to 256, with West Indies left-hander Shivnarine Chanderpaul left high and dry on 87 and Ed Cowan, named in Australia's 16-man Ashes squad overnight, then guided Notts to the close at 28 without loss, adding 18 himself.
Sussex left-arm spinner Monty Panesar went wicketless as Gary Wilson's second championship ton helped Surrey to 301 for seven at the Oval.
South Africa skipper Graeme Smith again failed to reach double figures but Ireland international Wilson replaced him at the crease and struck 124 to set up a solid foundation.
England paceman Anderson had to wait until the final hour of the day before picking up a pair of wickets in Lancashire's Division Two clash with Kent at Old Trafford.
While the hosts struggled with the bat, Anderson did not make a breakthrough until he first bowled top-scorer Mike Powell (57) before Matt Coles offered a catch to Simon Kerrigan soon after.
Brendan Nash added 50 as Kent reached the close on 216 for eight.
Northamptonshire continued their fast start to the new season as in-form quicks David Willey (four for 71) and Steven Crook (three for 47) ripped out Gloucestershire for 192.
Northamptonshire were 107 for three in reply at Bristol.
Hampshire opener Jimmy Adams (151no) batted through the day as Hampshire piled on the runs against Worcestershire at the Rose Bowl.
Hampshire closed on 367 for six with only Moeen Ali's three for 77 offering the Pears relief.
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