Borthwick was at the crease as the home side at Chester-le-Street resumed needing 147 with eight second-innings wickets standing, and although Ajmal Shahzad removed both Michael Richardson and Calum MacLeod to take his tally for the match to eight dismissals, the 24-year-old stood firm.
The game was won with the number three just short of a first century of the campaign and captain Paul Collingwood 35 not out, and Durham now trail the leaders by just five points with a game in hand.
Skipper Adam Voges and James Franklin both reached three figures as Middlesex cruised to a five-wicket victory over Somerset at Taunton.
Voges made 132 and shared a fourth-wicket stand of 200 with Franklin, who finished on 115 not out as the visitors eased passed their 402-run target despite Lewis Gregory removing both Sam Robson and Nick Compton early on.
Reigning champions Yorkshire comfortably held out for a draw against Warwickshire, for whom opener Ian Westwood fell 16 runs short of becoming the first man to make a century in both innings of a first-class game at Headingley.
The visitors declared on 219 for seven, setting their hosts 352 to win from 68 overs, and the captains eventually called it a day with Yorkshire having reached 221 for four.
Honours were even too at Southampton as rain denied Nottinghamshire the opportunity to claim victory over Hampshire at the Ageas Bowl, where only 9.4 overs were bowled.
In Division Two,??Lancashire??sit 13 points clear of Essex at the top after securing a tense final-day victory over??Kent??at Old Trafford by nine wickets.
Paul Horton’s 67 not out off 62 balls, with support from Alviro Petersen, who finished unbeaten on 22 , saw the home side reach their target of 104 with 14 balls to spare after the visitors had threatened to frustrate them.
Kent were eventually bowled out for 295 with Matt Coles and Adam Riley adding 49 for the eighth wicket, although Simon Kerrigan mopped up the tail after Kyle Jarvis and Peter Siddle had paved the way with four for 67 and three for 36 respectively.
Rory Kleinveldt was the pick of the bowlers as his four for 87 helped??Northamptonshire??to a 92-run victory over??Leicestershire??at Grace Road, in the process ending a run of 20 County Championship games without success.
Niall O’Brien top-scored for the home side with 58, helping to put on 59 for the fifth wicket with Ned Eckersley, in a total of 283.
Mark Footitt and Billy Godleman combined to steer??Derbyshire??to a seven-wicket win over??Gloucestershire??at Bristol.
Paceman Footitt took three of the last three Gloucestershire wickets to fall to record match figures of nine for 166 to leave the visitors needing 142 off a minimum 53 overs.
Godleman and Ben Slater put together an opening partnership of 81 with the former eventually going for 51 and the job all but done.
There was no play at all because of rain on day four at the Oval as the match between??Surrey??and??Essex??was drawn.