The highly-rated leg-spinner posted impressive figures of four for 37 in 15 overs as Worcestershire slipped from 145 for two to 205 all out, with Borthwick starting the collapse, halting Phil Hughes' confident progress to 87 from 136 balls.
From the time the Australian was adjudged leg before, pushing forward to Borthwick's fourth delivery, Worcestershire lost eight for 60 and Durham continued to turn the screw with their openers making 67 without loss in their second innings.
Mark Stoneman cruised to an unbeaten 41 from 60 balls and Will Smith (20 not out) survived an early chance in the slips as Durham expanded their lead to 105.
Middlesex were made to pay for dropping both Adam Voges and Chris Read, with the duo helping Nottinghamshire to a 231-run first innings lead after day two at Uxbridge.
Voges was dropped on 11 by Ollie Rayner at second slip off Toby Roland-Jones and the Australian went on to make 105 while Read was given a life on 15 when Gareth Berg failed to take a sharp chance at cover point off Corey Collymore.
Nottinghamshire's captain profited from his drop by making 71, also sharing a partnership of 143 with Voges before the visitors were all out for 329, with Tim Murtagh and Roland-Jones taking four wickets apiece before the inclement weather ended play at tea.
An unbeaten hundred from Steven Croft helped Lancashire take a stranglehold on their game against Surrey at Guildford.
Croft, the 27-year-old all-rounder, hit the fifth century of his first-class career and was unbeaten on 104 from 167 balls before play ended at 3pm, with the Red Rose on 425 for seven.
Ian Bell's decision to return to championship duty was rewarded with a dominant 57 for Warwickshire, who reached 175 for three after deciding to bat on a rain-shortened first day of their encounter with Sussex at Edgbaston.