The first half was a tight, tense affair. Saints got off to a good start, getting the ball to Dom Waldouck, Jamie Elliott and Calum Clark for early charges and winning a kickable penalty with just three minutes on the clock.
However, and in a situation which would be repeated following Lamb's second success seven minutes later, Saints failed to capitalise on the points by missing the kick offs. On both occasions the visitors allowed Leicester to put themselves in scoring positions and were fortunate to not concede points.
In the first instance some desperate defence stopped Niall Morris, Martin Castrogiovanni and Ben Youngs. And then they had George Ford to thank when the fly half made the first of his three first half misses.
The stiff breeze and inevitable intensity made the kicking game even more important as usual, and in the opening exchanges this too was evenly matched. Bombs from Geordan Murphy and Scott Hamilton put Saints under pressure, while a similar effort from Lamb ended up creating the fly half's second shot at the sticks.
Murphy failed to collect, and when Soane Tonga'uiha put the pressure onto Castrogiovanni at the scrum up went the referee's arm and Lamb landed the three points.
Ford's first and second miss came in successive attacks, but at the third time of asking he eventually got off the mark following Waldouck's breakdown infringement.
Having conceded Saints then proceeded to work themselves into a promising position. But Tigers first put pressure on in defence to win the ball back then within a couple of phases were back on the visitors' line.
Morris's kick ahead forced Lamb to concede a five-metre scrum, but although Leicester got the nudge on the ball was shifted away from the set piece and Saints' defence got to work, pushing the Tigers back in repeated phases and eventually winning the ball back through a great Tom May tackle.
Nevertheless Leicester still came away from the attack with another shot at the sticks, but with Ford again missing to the right the Tigers were probably feeling like they were not getting the reward their effort deserved.
However Saints did not punish this profligacy, despite winning a lineout against the throw five metres from the home line. Phil Dowson went on a charge, and had Waldouck managed to get the ball away before the hit then his team mates would have had an overlap.
Lamb sent a drop goal shot wide, and had his chip over the Tigers' defence come off then Saints could have had a try. But instead it was Lamb's opposite number who had the last say of the half, converting a penalty which tied things up at six all.
While the first half had been 40 minutes of limited chances, Leicester created and finished a try within 90 seconds of the re-start.
Again the genesis of the opportunity had been Saints' inability to collect a re-start cleanly. Ford's kick off bounced off a visitor to give Leicester a lineout, and after the Tigers went through a couple of phases half-time replacement Vereniki Goneva came into the line at pace and fed Matt Smith with a lovely pass for the score.
Ford converted and all of a sudden Saints, who had led for all bar three minutes of the match so far, found themselves with a seven-point deficit. Lamb pulled three points back almost immediately with a penalty, but although his next shot hit the upright Saints were finally showing what they could do, not least because from the kick off they set up a rolling maul, won a penalty and created a platform in the home half.
Both George Pisi and May had good runs and there was purpose and direction with ball in hand. So it was somewhat unfortunate that the next points came from Ford's right boot following Mike Haywood's late tackle on Murphy after the full back had sent a kick to the home 22.
It was a rare mistake from the hooker, who was showing increased commitment in defence and attack, not least when running from a ruck and sending Tonga'uiha off on a trademark charge.
For all the effort Saints were not getting into striking range, and when the contest entered its final quarter the visitors had Ford to thank again for keeping them within reach, the fly half missing two more penalties in quick succession.
Lamb, on the other hand, maintained his good day off the tee, rewarding a powerful rolling maul seven minutes from time with his fourth success from five attempts. However the fly half was yellow carded a couple of minutes later for blocking Anthony Allen as the centre was chasing a box kick, and Leicester played out the remaining time.
3mins SAINTS Pen Lamb 0-3
10mins SAINTS Pen Lamb 0-6
12mins LEICS Miss pen Ford
14mins LEICS Miss pen Ford
17mins LEICS Pen Ford 3-6
25mins LEICS Miss pen Ford
32mins SAINTS Miss DG Lamb
40mins LEICS Pen Ford 6-6
HALF-TIME LEICESTER 6 SAINTS 6
41mins LEICS Try Smith Con Ford 13-6
45mins SAINTS Pen Lamb 13-9
48mins SAINTS Miss pen Lamb
53mins LEICS Pen Ford 16-9
65mins LEICS Miss pen Ford
67mins LEICS Miss pen Ford
73mins SAINTS Pen Lamb 16-12
76mins SAINTS Yellow card Lamb
FULL-TIME LEICESTER 16 SAINTS 12