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Sebastian De Chaves gave the home side an early lead as he was on hand to scramble the ball over the line from close range, after the Tigers forwards had got to within a few metres of the Northampton try line.
Laurence Pearce then added a second try 20 minutes later when he capitalised on some fine work from Jack Roberts, who made a break through the Saints defence.
In the second half, winger Howard Packman darted across the try line to give the Saints some hope, but they could not add to their score in a physical and gruelling match.
A late Owen Williams penalty confirmed victory for the hosts as Leicester won the Midlands derby.