After electing to bat, Durham stalled when Tom Bailey took two of his four wickets to reduce the hosts to 46-2.
But Borthwick made his best score in two summers (134), sharing a stand of 88 with Jack Burnham (43).
Paul Collingwood then made an unbeaten 85 to help Durham close on 341-6.
Just 11 days short of his 40th birthday, the former England international batted more than three hours, putting on 134 for the fifth wicket with Borthwick, who holed out at long-on off spinner Simon Kerrigan.
Bailey, who was only in as replacement following Jimmy Anderson's return to Test duty this week, induced edged catches from both openers in an impressive eight-over opening spell.
He then picked up his fourth wicket late in the day, when Ryan Pringle gloved an attempted hook to slip, giving Liam Livingstone his third catch.
Durham century-maker Scott Borthwick:
"It's a decent pitch and I felt in pretty good nick from the start. I didn't score many in the first two games, but I didn't feel in bad form.
"A few low scores play on your mind, so it's good to put them behind me. I got out three times in the 90s last year so I was a bit nervous approaching my hundred.
"Once I got there I was determined to go on and I was disappointed with the way I got out."
Lancashire's Tom Bailey:
"It is tough to step into Jimmy Anderson's shoes and I'm happy with four wickets, although I'd rather see the side win.
"Our aspirations are to win the Championship and to have a chance of winning this game we will have to come back strongly in the morning.
"There was a bit of swing early on, but the pitch isn't offering much."
Durham's Scott Borthwick more than doubled his County Championship run haul for the season to help his side into a good position against in-form Lancashire at Chester-le-Street.