Leicester thought they had a try back when Hamilton flung himself at the line but Jon Clarke got under the wing and referee David Pearson ruled it out after consulting the TMO.
A close range Myler penalty made it 17-0 before Tuilagi hit back after good work from Ben Youngs and Geordan Murphy, Toby Flood adding the conversion.
But Northampton would have been clear at the break had Myler not missed three penalties, and he was thankful that Jeremy Staunton was equally wasteful after replacing the injured Flood just before the break.
After Myler missed another kick, Saints opted to replace him with Geraghty and the England man made an instant impact by starting a move finished by Mujati and adding a conversion and then a penalty after George Chuter was sin-binned for killing the ball.
Chuter was followed down the tunnel by Dylan Hartley for the same offence and although Hamilton scored down either wing in the space of three minutes late on, Northampton kept their nerve.
Northampton director of rugby Jim Mallinder told BBC Radio Northampton: "It was a combination of forwards and backs working together. It gives us all sorts of options.
"I thought the props played well. The pack was really good.
"The pressure was on us as it was a home game. We started well, Leicester came back as we knew they would but it was really pleasing to come out with a 'W'."
Leicester rugby director Richard Cockerill said: "The start was unimpressive from us. The laws dictate that you carry the ball and you cannot easily defend against that.
"We were in the game, but we were also indisciplined, conceded too many penalties and we did not look after the ball well enough. They did those things better than us.
"By the time we got to grips with holding onto the ball, we could have come away with two points from a fourth try. I've no complaints about the result or the referee. But on the performance, two points would have been more than we deserved."
Northampton: Foden, Ashton, Clarke, Downey, Reihana, Myler, Dickson, Tonga'uiha, Hartley, Mujati, Lawes, Day, Dowson, Wood, Wilson. Replacements: Ansbro for Clarke (69), Geraghty for Myler (56), Dreyer for Tonga'uiha (69), Mercey for Mujati (70), Easter for Lawes (76), Sharman for Dowson (69), Clark for Wilson (69). Not Used: Powell.
Sin Bin: Hartley (69).
Leicester: Murphy, Hamilton, Hipkiss, Allen, A. Tuilagi, Flood, Youngs, Ayerza, Chuter, Castrogiovanni, Green, Skivington, Newby, Woods, Waldrom. Replacements: M. Tuilagi for Hipkiss (62), Staunton for Flood (39), Grindal for Youngs (70), Stankovich for Ayerza (63), Pienaar for Chuter (76), Cole for Castrogiovanni (56), Slater for Green (63), Duffey for Newby (69).
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