The home side was all out for 292 just before the close with Hain the last to fall for 130. The accomplished knock continued the 26-year-old’s excellent red ball form, his last four championship innings having brought 449 runs for twice out.
After choosing to bat, the Bears leaned heavily on Hain as other batsmen got in but then found ways of getting out against a Red Rose attack which persevered well on a good batting pitch.
Hain found some support from Michael Burgess (41), but Lancashire’s bowlers, with Kiwi seamer Will Williams impressing on his debut, kept taking wickets at important times.
Williams closed with 24-11-42-2 and the pressure he built, contributed to wickets taken by his colleagues, notably Danny Lamb (three for 43) and George Balderson (three for 68)
The Bears lost two early wickets against a well-directed new ball attack in which Williams conceded just three singles in his first seven overs. That pressure led to errors as Alex Davies tried to pull a good-length ball from Tom Bailey and spliced to short extra cover and Rob Yates chopped an attempted drive at Balderson on to his stumps. Balderson also dismissed Dom Sibley (28, 70 balls) who edged an away-swinger to wicketkeeper Dane Vilas.
Hain and Rhodes dug in to added 65 in 21 overs before Williams bagged a deserved first wicket when a perfect outswinger took a thin edge from Rhodes (23, 63 balls).
When Matt Lamb was bowled through a drive by his namesake Danny, the Bears were 142 for five, but Hain and Burgess responded with the most fluent batting of the day. Burgess advanced to 41 (72 balls) before lifting a short ball from spinner Matty Parkinson to extra cover.
Hain reached his 14th first class century with successive fours off Parkinson but continued to lose partners as Danny Briggs fell lbw to Lamb and Henry Brookes edged Williams to second slip.
Liam Norwell, back in the side after injury, reached 1,000 first class runs when he clouted Williams for four to get off the mark, but was then bowled by Lamb and Lancashire’s satisfying day concluded in the final over when Hain edged Balderson into the cordon.
Rachin Ravindra produced a debut to remember for Durham, scoring a career-best 178 not out as the home side piled up 375-3 on day one against Worcestershire.
The New Zealander was only signed by Durham for one match after Keegan Petersen’s premature departure, but certainly made an impression for the North-East outfit with a sublime unbeaten hundred, his fourth in first-class cricket.
He shared a mammoth stand of 230 with Scott Borthwick, who notched 96, for the second wicket.
Seamers Charlie Roberts and Ben Gibbon and spinner Josh Baker picked up a wicket each on a testing day for the visitors’ bowling attack.