Tries from Tom Collins, Courtnall Skosan, Sam Matavesi, George Furbank and Tom James ended the black, green and gold's four-match losing streak, in some style.
Saints built the performance on solid defence, starving the Falcons of opportunities in the away 22.
And Boyd's side took their chances when they came as they racked up a big victory that lifted them up to fifth in the Gallagher Premiership.
"We did certain things well at different times but over the 80 minutes we were certainly very happy to come here and get five points because we haven't done that very often of late," Boyd said.
"We had a healthy lead at half-time from a couple of reasonably long-range tries and then managed to build on that.
"There was a lot to be happy with."
Boyd added: "The defence was a very big plus today.
"The guys worked hard, got connected and we didn't concede easily.
"We controlled the middle of the ground a lot better so we didn't allow them into our back third as often as we have in the past few weeks.
"If you control the ground, you control the momentum and the pressure, and if you're patient you'll get some crumbs."
On a day when Gloucester won at Saracens and Harlequins edged out Exeter Chiefs, Saints knew a victory was vital in their pursuit of a top-four spot.
And Boyd said: "It keeps us in touch.
"With the other results, we're now fifth and you don't want to be going backwards in the ladder.
"We've stopped talking about that (league position) and concentrated on our performance, but this was an important win."