The Saracens and England skipper twice elected to go for tries instead of taking penalty shots at goal with the game balanced at 12-12.
And the decisions paid off as first Rod Penney went over on 65 minutes with Saints down to 14 and Ben Foden in the sin-bin.
Michael Owen then turned the screw with a second try after Saints also had Dylan Hartley yellow-carded.
Borthwick said: “I knew they would be disrupted by just having Ben Foden sin-binned for not releasing, so I went for it.
“We had a quick chat, because I believe it’s hugely important to know what your players feel in such situations. But they backed us to go for the try and the lead.
“It was my decision as captain, but with the support of the lads. I also made the call not to go for a try or chase the bonus point when we got another penalty near the end.
“We didn’t have time left to score two tries, so I went for the three points to boost our points-difference.”
Saracens are now fourth ahead of Quins — on points-difference.
Saints boss Jim Mallinder said: “Once we lost Ben to the bin, it tilted the balance their way. But I give Saracens credit. Our defence was the better of them for an hour, but they kept coming.”