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Alistair Hargreaves scored a try for Saracens just before the half-hour mark, but was then shown a yellow card just before half-time for killing the ball.
Two penalties late in the first half for the visitors made it level at 14-14 at the break.
Hodgson kicked Saracens to to a 12-point lead with less than 10 minutes to go.
Charlie Davies gave Wasps late hope with a 77th minute try.
However, Saracens held on to move up to second in the table while Wasps remain eighth.