Durham 364 for 4 (Lees 171, Bedingham 138) trail Derbyshire 443 (Guest 197, Madsen 62, Borthwick 4-25) by 79 runs
The pair added 305 from 333 balls for the third wicket, Durham's best, and at stumps on day two the visitors were 364 for 4 ,some 79 runs behind Derbyshire's first-innings 443.
Durham had earlier been on the receiving end on a flat pitch as Guest and the tail took advantage of some poor bowling. Derbyshire added 126 runs in 25 overs with Guest and Conners doing most of the damage by plundering 71 from 48 balls.
Guest reached his 150 by turning Ben Raine behind square for his 23rd four before the Durham seamer got one to straighten and knock out Alex Thomson's off stump.
Zak Chappell gloved a Brydon Carse lifter to short leg but Durham lost control once Guest and Conners engaged the turbo.
Conners pulled Carse for six and after Derbyshire picked up five penalty runs when the ball struck the helmet behind wicketkeeper Ollie Robinson, he drove Matthew Parkinson over the long off boundary.
Durham were looking increasingly ragged until Conners charged Scott Borthwick and was stumped for 33 off only 25 balls.
Guest had a double-century in his sights but when he took on Borthwick, he failed to clear Raine at long on.
It had been an outstanding innings and one that looked even better when Conners struck twice in the fourth over after lunch.
Michael Jones was bowled as he shaped to play through midwicket and Borthwick was caught on the crease but Lees and Bedingham responded with a thrilling counter-attack.
Bedingham lit the fuse by pulling Chappell for six before Lees straight drove Thomson for consecutive sixes.
Lees drove Anuj Dal back over his head for another six and his only anxious moment came on 79 when he almost edged Chappell behind.
But he drove the next ball for four and then turned Chappell for a single to reach that 1,000 milestone which was quickly followed by his fourth century in five innings when he clipped Dal to the fine leg boundary.
Lees had faced only 127 balls but Bedingham reached his hundred off only 113 when he edged Luis Reece to third man for his 15th four.
The runs kept coming and the pair passed Durham's previous highest third-wicket stand of 243 which they had set at Leicester at the end of June.
Lees went to his 150 with successive fours off Nic Potts but the stand was finally broken when Bedingham clipped Dal to substitute fielder Mitch Wagstaff at short midwicket.
Durham sent in Migael Pretorius to take advantage of a tiring attack but Conners returned to remove Lees, who was caught behind driving at a wide ball two overs before the close.