As Lancashire closed day one on 272 for eight at the Emirates Old Trafford, Jennings became the first batter in this fixture's history to score four hundreds in as many innings.
Jennings made 119 and fellow opener Luke Wells 84 as Lancashire advanced to 180 without loss just before tea only for Yorkshire to launch a fightback.
Wells was Hills' first victim and Jennings was later the first of five wickets to fall for 20 runs as the Red Rose slipped to 251 for six - all to Hill's skilful seam - while Ben Coad took the day's last two wickets.
Hampshire opener Felix Organ maintained his fine form with 71 as his title-chasing side reached 229 for five on the opening day against Northamptonshire at the Ageas Bowl.
Organ ended the Royal London Cup with a 54 in the semi-final against Kent Spitfires, having scored 72, 118, 41 and 65 in his last four Championship matches.
Against Northamptonshire, he put on 50-run stands with Joe Weatherley and Nick Gubbins, while visiting bowler Jack White claimed two for 35.
Essex's Matt Critchley will resume on 80 as his side reached 327 for four at stumps after being put into bat by Kent at Canterbury.
Critchley cashed in after being dropped on six after Sir Alastair Cook made 78 and Tom Westley 54.
The contest had looked even when Essex were reduced to 219 for four, but Critchley's unbroken partnership of 108 with Feroze Khushi (46 not out) tipped the momentum back in the visitors' favour.
Australia opener Marcus Harris hit 159 as Gloucestershire ran up 320 for six on the first day against arch-rivals Somerset in Taunton after being put into bat on a benign wicket.
Left-hander Harris's 263-ball knock included 17 fours and a six and was his third Championship century of the season.
Ben Charlesworth contributed 56 to an opening stand of 126, while Ollie Price weighed in with 52 against a Somerset attack featuring Pakistan off-spinner Sajid Khan, who finished with none for 64 on his debut.
Division Two leaders Nottinghamshire lead by 123 runs after 20 wickets fell on the opening day of their match with bottom-of-the-table Leicestershire.
Nottinghamshire were bowled out for 201, losing their last eight wickets for 118 as they collapsed from 83 for two just after lunch, Chris Wright and Ed Barnes taking three wickets each.
Leicestershire found conditions no more to their liking, dismissed for just 93 in reply, with home bowlers Luke Fletcher (four for 23) and Brett Hutton (three for 32) doing the damage. Nottinghamshire are 15 without loss in their second innings.
Worcestershire closed day one in Cardiff against promotion-chasing Glamorgan on 285 for seven, with Gareth Roderick unbeaten on 88.
Roderick shared a 127-run fifth-wicket partnership with Ed Barnard (75) to lift the visitors from 114 for four to 241 for five, with Glamorgan seamer Timm van der Gugten taking three for 42.
New Zealand Test bowler Ajaz Patel trapped Barnard lbw for his first wicket on his Glamorgan debut.
Leus du Plooy enjoyed another good day at Durham's expense as Derbyshire recovered from 58 for four to reach 306 all out at the Incora County Ground.
Division Two promotion hopefuls Derbyshire were struggling until South African Du Plooy followed his two centuries against Durham at Chester-le Street in July with 82 from 123 balls.
Harry Came scored a career-best 78, sharing a stand of 143 in 32 overs with Du Plooy, before Anuj Dal added 56, with Durham pair Chris Rushworth and Ben Raine both taking three wickets.