Durham 445 (Clark 100, de Leede 65, Coughlin 59*, Borthwick 53) and 272 for 4 dec (Jones 121*) beat Gloucestershire 292 (Charlesworth 71, Harris 52, Patel 5-113, Potts 3-43) and 300 (Harris 122*, Patel 5-96) by 125 runs
Harris carried his bat to finish unbeaten on 122, off 195 balls, with 15 fours. But it was never going to be enough as New Zealand Test left-arm spinner Patel followed up his five for 113 in the first innings with five for 96.
Gloucestershire were bowled out for 300 before lunch on the final day and remain in search of a first win. They took four points from the match, while Durham's 23 from a fourth victory in six games strengthened their lead at the top of the table.
At 181 for six at the start of play, the hosts required an unlikely 245 to win. But Harris was unbeaten on 71 and his team could take some encouragement from clear blue skies and a placid batting surface.
Matt Taylor helped Harris add 21 to the total, but with his score on 12, he missed a defensive prod and was pinned lbw by Patel, who bowled the first 11 overs of the day from the Pavilion End.
Harris looked to survive a difficult chance off Patel on 90 when he edged a ball at ankle height just out of the reach of slip Matthew Potts.
It was all the good fortune the left-handed opener needed to reach three figures off 163 balls, advancing down the pitch to hit Patel over mid-on for the 13th boundary.
Shaw provided solid support and gradually grew in confidence, smacking Patel to the long-on boundary and then pulling Ben Raine for another four.
A single to square-leg off Bas de Leede took Shaw past his previous best first class score of 42, but he had added only a single when snapped up by Potts at slip off a Patel delivery that turned from outside leg stump.
Shaw had hit six fours and a pulled six off Scott Borthwick, but his departure signalled the end of any slim Gloucestershire hopes.
Zaman Akhter lasted only four deliveries before being bowled by Potts, who finished with three for 43 from 19.2 overs.
Ajeet Dale hit a couple of defiant boundaries before being last man out, caught at cover to give Patel his fifth wicket of the innings and tenth of the match.
Harris walked off undefeated, but the Australian's valiant efforts only served to highlight the batting frailties of team-mates in an injury-hit side.
Durham could take plenty of positives from another impressive display, which will take them into the switch to T20 cricket in great heart.