Borthwick and Gordon Muchall shared a fifth-wicket stand of 118 to put Durham in a commanding position.
It did not look good for Durham when the pair came together at 13-4 but their fifth-wicket stand ensured the County Championship leaders ended the day in control. They eventually closed on 168-6, with Muchall unbeaten on 66 and Paul Coughlin five not out, which gives the visitors a lead of 268.
Sussex began day two on 44 for two with Matt Machan 11 not out and Ed Joyce nought not out.
Machan added just ten to his overnight score before he was superbly caught by Keaton Jennings off the bowling of Graham Onions.
Luke Wright was then out for five when he was caught behind by Michael Richardson to give Chris Rushworth his third wicket of the innings.
It did not get any better for Sussex as Ben Brown fell for 15 to leave them 91-5.
Ed Joyce brought the hundred up for his side with a boundary but then went the very next ball when he picked out Jennings at gully off John Hastings.
The seventh Sussex wicket fell ten minutes before lunch when Chris Nash played round a straight one and was clean bowled by Rushworth.
Shahzad then became Rushworth’s fifth victim of the innings with the last ball before lunch.
Early in the afternoon session, Rushworth claimed his sixth wicket of the innings when Steve Magoffin nicked one straight to Paul Collingwood at first slip.
Sussex did manage a late onslaught with the two new loanees George Dockrell and Tim Linley offering resistance. They put on 40 for the final wicket and that was just enough to help their side to a batting point.
Dockrell ended unbeaten on 37 and was the top-scorer but when Linley picked out mid-wicket on ten he was left stranded and Sussex were all out for 201.
Rushworth was the stand-out performer with the ball and claimed 6-49 in 21 overs.
Durham, who went into their second innings with a lead of 100, did not start well with the bat. Magoffin ran in and produced a fine first over as he dismissed both Stoneman and Jennings in four deliveries.
Stoneman nicked one to Luke Wright at third slip, while Jennings was caught behind with neither troubling the scorers.
It got better for Sussex when Magoffin sent Collingwood’s middle stump flying to leave Durham 11-3.
Magoffin then rounded off a fine first 16 balls when he got one to nip back through the defences of Richardson to leave Durham in all sorts of trouble.
But Richardson and Muchall helped their side to 131-5, from 13 for four, with a partnership of 118.
Richardson went for 74 when he was bowled by Wells, while Muchall remains unbeaten and is yet to be dismissed in the match as, after his 81 not out in the first innings, he was unbeaten on 66 at the close.
Ryan Pringle was bowled by Tim Linley for 15 late on in the day but Sussex have it all to do in the final two days if they are to come out on top.
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