The first try of the game fell to the hosts as a chip over the top in the 13th minute set up Christian Wade, who bundled through and crossed over.
Moments later, Wasps were 17-3 up following a good finish from Elliot Daly and the subsequent Andy Goode conversion.
The Saracens comeback started on 22 minutes when Jackson Wray crossed over from a driving maul, and, following another Alex Goode penalty, Chris Wyles went over despite Wade's best efforts to hold him up.
The visitors were 17-20 up at the break and it would become a war of attrition after the restart, with the scoreline so finely poised.
As it was, no further tries were to come, but Alex Goode sent another two penalties between the posts in the second half to complete a fine comeback victory for Sarries.