It was a performance as impressive for the Saints' defence and discipline throughout the match as for first half tries for James Downey and Paul Diggin, and the visitors were restricted to just one penalty goal all afternoon before Scott Armstrong added gloss to the scoreline with the Saints' third.
It was a stunning start for the Saints, who ran home a length of the field try after receiving the kick off. Keeping the ball in hand, Downey and Jon Clarke made telling inroads, as did James Craig on his first competitive start for the club. There was pace and accuracy in the passing and it was all too easy for Downey to re-join the move and glide over - the clock not yet showing two minutes.
The conversion from close to the touchline was a real confidence booster for Lamb, as was the period of Saints tackling that eventually forced an error from Exeter - epitomised by Christian Day's crunching hit on Sireli Naqelevuki.
A penalty followed from the scrum and while Lee Dickson's quick tap ended with Scott Armstrong forced into touch, the Saints' attacking intent was clear. Despite a penalty miss from Lamb, the Saints were making everything go their own way and Exeter's first spell of pressure ended in a turnover, the Saints' fourth inside the opening quarter.
Momentum was maintained by the Chiefs, but for a ten minute spell in Saints territory, they only had one Ignacio Mieres penalty to show for their efforts and the Saints swept up field in clinical fashion. A booming penalty to touch from Greig Tonks put them to halfway and Scott Armstrong tracked the play to cut through defenders. That followed a patient string of phases and when the ball came back Lamb smartly slid a grubber through that Diggin latched onto on the slide.
Lamb was good with the wide conversion once more and just three minutes later further extended the Saints advantage to 17-3 with a penalty - Exeter cynically killing the ball. When a similarly pre-meditated moment of indiscipline saw Chiefs' Luke Arscott yellow carded, the Saints had 10 minutes at 14 men and pressed home the advantage to the tune of another Lamb penalty before the break - a well-deserved 20-3 lead.
Exeter came out needing and looking for an early score, but after turning up a shot at the sticks in favour of going to the corner, a duo of turnover penalties earned by Calum Clark and Mike Haywood helped the Saints clear.
They would move further clear on the scoreboard too, Lamb kicking a third penalty of the afternoon and in defence they continued to come up with all the answers for the Chiefs threat. That took them past the hour mark still with just the three points against and Lamb kicked his side four scores clear in the 68th minute, a sixth success of the match.
They were in no mood to just close out the game however and with three minutes to play, a Chiefs scrum was stolen and allowed Clarke to slide in Armstrong, who won the battle for the ball and leapt over for his first Premiership try for the Saints.
The bonus point was now looking a distinct possibility, especially when Tom May sent Armstrong racing down the left wing - but it wasn't to be and the Saints had to settle for the four-point win, a first since the opening afternoon of the season.
AVIVA MAN OF THE MATCH Ryan Lamb
REFEREE Greg Garner
2mins SAINTS Try Downey Con Lamb 7-0
9mins SAINTS Miss pen Lamb
21mins CHIEFS Pen Mieres 7-3
26mins SAINTS Try Diggin Con Lamb 14-3
29mins SAINTS Pen Lamb 17-3
33mins CHIEFS Yellow Arscott
40mins SAINTS Pen Lamb 20-3
HALF-TIME SAINTS 20 CHIEFS 3
55mins SAINTS Pen Lamb 23-3
68mins SAINTS Pen Lamb 26-3
77mins SAINTS Try Armstrong Con Myler
FULL-TIME SAINTS CHIEFS