Saints, thanks to a star performance from George Pisi, were in complete control as they opened up a 22-3 lead at the interval.
They carelessly lost control and received two needless yellow cards from referee David Rose, but Bath were ultimately unable to avoid a fourth consecutive defeat.
After last week's hammering at the hands of Leinster in the Heineken Cup, Bath responded favourably by having the better of the early exchanges and deservedly took the lead with a 13th-minute penalty from Olly Barkley.
The lead was short-lived, though, as minutes later the Saints scored the first try of the game.
Vasily Artemyev was the architect of the score, dancing past three defenders on the right flank to enable Northampton to outflank on the left, where Phil Dowson accepted the final pass for a try which Lamb was unable to convert.
The Bath defence was almost immediately breached again. Samoan Pisi made a huge hole in midfield and provided the scoring pass to the supporting Tom Wood, Lamb converting to leave Bath 12-3 down after 22 minutes.
Northampton nearly had a third try when Jamie Elliott crossed but he was recalled as the referee adjudged that there had been an earlier knock-on.
Pisi then produced an excellent kick and chase and though Nick Abendanon got back to save Bath, he was penalised for holding on and yellow-carded. Lamb kicked the resulting penalty.
With only 14 players, Bath struggled to hold a rampant Saints and another try was almost inevitable. A clever kick through from Lamb put the visitors under pressure before, from the resulting ruck, the outside half sent out a dreadful pass to Elliott but the winger was able to brilliantly scoop up the ball and dive over in the corner for a try which Lamb converted.
Early in the second half, Abendanon returned and immediately saw his side reduce the arrears to 22-6 with a penalty from Barkley. But there was to be no immediate stemming of the tide as following another strong run by Pisi, Stephen Donald was forced to concede a penalty and he collected Bath's second yellow card.
Elliott crossed the try line again only to be denied as the pass to him was ruled forward, which enabled Donald to return from the sin-bin with no damage done to the scoreboard in his absence.
Bath continued to battle tenaciously and received huge encouragement when the Saints received two yellow cards within a minute. Replacement Samu Manoa, who had only been on the field for two minutes, was first to go for collapsing a line-out and then James Downey followed for an offside offence. From the resulting scrum Francois Louw picked up to score a try which Barkley converted.
Lamb then missed a 25-metre penalty as Northampton nerves began to jangle but amazingly the Saints, with only 13 players, had much the better of the next 10 minutes and comfortably held on for a deserved win.
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