Full-back Goode, back from duty with England Saxons, slotted five penalties on Sunday to make sure the defending champions, who were guilty of failing to make superior possession tell, at least secured victory with some comfort. Wing James Short was the only man to cross the tryline for Sarries.
The victory puts Saracens three points behind leaders Harlequins, while Wasps hold a nine-point gap over bottom club Newcastle going into a run of tough matches against Exeter, Sale and London Irish.
Saracens were without five England internationals but they dominated the first half, with veteran Irish scrum-half Peter Stringer ubiquitous and industrious, and were unlucky to not be more than two points up after 40 minutes.
Wasps looked more lively in the second period as scrum-half Joe Simpson - who only arrived back from Rome on Sunday morning after acting as a non-playing reserve for England in Italy - joined the fray with 10 minutes gone.
Wasps showed 10 changes to their side as an injury crisis showed signs of abating, and they made an encouraging start as number eight Billy Vunipola and hooker Tom Lindsay crossed in the first 22 minutes.
Vunipola made some battering runs from the base of the scrum during the opening minutes and popped up on the left to take Riki Flutey's pass and touch down, with Nicky Robinson converting.
Sarries responded immediately, though, with two penalties by Goode from close range in the next five minutes, the first because of Vunipola leaping offside.
If the visitors felt those six points were scant reward for a period of pressure, they gained further from a stroke of luck shortly afterwards when Short snatched Vunipola's high pass and sprinted in from the halfway line for a score that Goode converted.
But Wasps struck back as Lindsay ran on to a kick from Robinson, on his return from a calf injury. The hulking hooker collided with the post but the video official confirmed that he held on as he went to ground. Robinson again added the extras to edge the hosts back in front.
Goode's third penalty ensured Saracens went in 16-14 ahead at half-time and he took the lead out to five points with another successful kick three minutes into the second period.
Robinson cut Sarries' advantage back to two points with a 68th-minute penalty but Goode's fifth penalty made the result safe.
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