Boyd's side scored six tries in a sensational 42-22 success against Gallagher Premiership play-off rivals London Irish, who were hosting a St Patrick's Day party.
But the home side's afternoon fell flat as Saints bounced back from going 8-0 down early on to secure a crucial bonus-point win that lifts them above London Irish in the league standings.
And Boyd said: "We could win one, two, three, four games and it's probably not going to move you much in the table, but we know it's still alive.
"We think we're still in control of our own destiny and it's one game at a time.
"We've got a tough game against Bristol next Saturday but we'll celebrate today's victory on St Patrick's Day.
"I might even have a Guinness!."
On how things panned out against Irish, Boyd said: "They say the classic game of two halves but this was a game of four quarters.
"It was a horrible first 20 minutes where we were probably still on the bus and didn't get it right.
"It was a pretty decent fightback where we steadied the ship.
"The third quarter was pretty compelling and the last 20 minutes was hanging on when we ended up playing with 13 men.
"It would have been disappointing to concede a bonus point to them at the end but we hung on and it was a pretty good day at the office really.
"TC (Tom Collins) had a good day and he's as dangerous as. He bounces around all over the place, but it would be very unfair to pick out anybody because we knuckled down and got our process right.
"It was a pretty good shift from the forward pack and there was some good control in the backline, too."
"In the case of Courtney and Dan, that's why one's a centurion for his country and the other is pretty close to it," Boyd said.
"We managed to get Courtney 15 minutes off at the end by putting Sam Matavesi to the back of the scrum, but they're true professionals.
"Courtney didn't come in until Thursday, he had a couple of days with his family, but he came back in and you very seldom get a bad day out of Courtney.
"Dan Biggar was in on Tuesday and rolled his sleeves up and got straight back.
"They contributed much the same as a number of other people but coming back from international duty, they put in a pretty good shift."