Saints' victory was never in doubt after opening up a 20-3 half-time lead courtesy of tries from centre James Downey and wing Paul Diggin. Both were created by Lamb, who finished with a 16-point haul by slotting two conversions and four penalties.
Wing Scott Armstrong rounded things off in the final moments with the hosts' third try.
Exeter, who had been third in the table entering this game, could only register an Ignacio Mieres penalty as they came off heavily second best at the breakdown as Saints' forward power proved too much to handle.
Northampton opted to attack from deep from the kick-off and it paid dividends as they crossed for the opening try inside two minutes.
Centre Jon Clarke was freed down the left by Lamb's pass, before flanker James Craig took the move on for the ball to be worked right for Downey to slide over. Lamb added the extras for a 7-0 advantage.
More good work by Lamb opened space for Armstrong, although the former London Irish man was off target with a ninth-minute penalty effort.
Exeter hit back with two prolonged attacking phases, with centre Sireli Naqelevuki featuring prominently, and fly-half Mieres got them on the board when he slotted a penalty at the end of the first quarter.
The Chiefs enjoyed more pressure in the Saints 22, but it was the hosts who were next to cross the line as enterprising link play between Armstrong and Greig Tonks paved the way for Diggin to dot down from Lamb's exquisite grubber, with the fly-half's conversion going over with the aid of the crossbar.
A long-range penalty then saw Lamb further extend the hosts' lead, and the visitors' predicament got worse when Luke Arscott was yellow-carded for a deliberate knock-on.
Lamb's second penalty just before half-time saw Saints turn the screw after their pack had given the Chiefs' front row a thorough work-over at a series of scrums, and opened up a handsome 17-point advantage.
More Exeter scrum woe allowed Lamb to register the first points of the second stanza with his third penalty of the contest in the 55th minute.
The Chiefs' difficulty in combating Northampton's physicality at the breakdown saw them struggle to string threatening phases together despite having swathes of possession, with their best opportunity seeing replacement Kevin Barrett spill the ball as he attempted to wriggle over.
Lamb went on to add his fourth penalty before Armstrong rounded things off by getting to Clarke's delicate kick through for a try converted by replacement Stephen Myler.
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