After starting the season with a draw in their opening Prem game, Saints reeled off four wins in a row to go top of the table before suffering a first defeat away to Bristol Bulls, which dropped them to third.
But they bounced back last weekend with victory in Pau in a positive start to their Champions Cup campaign.
“We’ve got an incredibly talented playing group which I feel still has so much more to offer, supported by brilliant people across the club who are fully invested in what we’re building,” said Dowson.
“This coaching team is a big source of enjoyment for me; the cohesion, trust and balance we share is special, and we’re having a lot of fun doing it.”
Former Leicester full-back Vesty joined Saints as an attack coach in 2018 before being promoted to his current role.
He said: “I feel like I am a different coach to the one who started here seven years ago. I’m definitely still learning and I’ve matured as a coach, but fundamentally my passion remains the same; I’ve always wanted to help people get better and that’s still the most rewarding part of the job.”
Craig, like Dowson, is a former Northampton player, making 73 appearances before retiring in 2019. He joined the senior coaching team three years later.