The 24-year-old pressed his case to keep his place in the England Test side with a fluent 87 before being caught behind off seamer Chris Liddle.
Earlier, David Payne's quickfire 28 off 33 balls helped the hosts post 303.
Jennings and South Africa batsman Stephen Cook hit half-centuries as Durham closed on 270-4 trailing by 33.
The pair shared a 114-run opening stand for the visitors before the latter edged to first slip off Liddle on 64.
Jennings' knock included 12 fours and a six but the England batsman fell 13 runs short of a second successive century in Championship matches.
Craig Miles took two wickets in two overs late on to peg Durham back as they looked to build a first innings lead.
Keaton Jennings continued his fine start to season with the bat to help Durham take control against Gloucestershire on day two at Bristol.