Borthwick was unbeaten on 54 at the close after Durham had slumped to 49 for four against some tight County bowling under floodlights, with Ben Sanderson claiming two scalps.
The visitors finished the day on 108 for four after a 59-run stand between Borthwick and Graham Clark.
Luke Procter though made a gutsy 76, combining in a partnership worth 66 with an aggressive James Sales in the afternoon session.
Matthew Potts who was expensive early on responded well to take four wickets and wrap up the tail as the County were bowled out for a disappointing 183 having won the toss.
Although Northants' batsmen found the boundary frequently during their innings, several were guilty of lack of judgement outside off-stump and lost wickets at regular intervals.
Showing his trademark metronomic accuracy, Rushworth found plenty of movement to beat the bat.
He removed Ricardo Vasconcelos early who edged behind to give keeper Ned Eckersley the first of five catches.
Emilio Gay too was caught behind but off his glove down the leg side, and in-form Rob Keogh gave Rushworth his third wicket when he edged to Paul Coughlin at third slip who took a good low catch.
Saif Zaib also edged behind playing a loose drive off Ben Raine in what was becoming a familiar story.
Skipper Adam Rossington played a couple of aggressive boundaries but was adjudged lbw after leaving a ball from Potts and Northants were in trouble at 91 for five at lunch.
Procter though was unbeaten at the interval.
He had played some crunching drives and was particularly harsh on Potts, smashing him down the ground and driving him to the long-on boundary before rocking back and pulling a short ball dismissively through midwicket.
Potts removed Harry Gouldstone soon after lunch, but 18-year-old Sales, who hit the winning runs against Surrey on debut last week, got into his work quickly with a string of boundaries.
He pulled Potts confidently through midwicket for four and drove Raine through extra cover.
Procter dispatched spinner Liam Trevaskis over wide long-on for six, but his vigil came to an end after 136 balls when he nicked the spinner behind.
Northants then lost their last three wickets for just one run in nine balls with Potts claiming two in one over. Sales remained undefeated on 38 from 81 balls.
Sanderson struck in the first over of Durham’s reply, bowling Alex Lees without scoring.
He then had Michael Jones lbw before Rob Keogh brilliantly ran out David Bedingham with a direct hit. The Durham right-hander had just reached 1,000 Championship runs for the season.
Then, when Sales had Eckersley lbw, Durham’s scoring had started to dry up.
Borthwick who had ferociously cut Procter through cover for four early on looked to regain the initiative by taking two boundaries off an over from Sales and started the fightback aided by Graham Clark who too found the ropes reaching 23 at the close.
Procter said: "It was tough early on. The pitch is not doing too much to be honest but they bowled really well so it was tough. When you are in you just have to keep grinding the runs out."
Asked about the state of the game, he added: "It is quite even to be honest at the minute. I think if we come in the morning and we get a few quick ones, we could bring ourselves back into it and maybe get on top.”
Play is due to resume on Monday morning at 10.30am.