Tony Watt and Liam Craig both squandered second-half penalties to underline Saints’ superiority against a struggling St Mirren side still searching for their first win under manager Oran Kearney.
After relying on single goals for home wins in recent outings, Tommy Wright’s dominant team had opportunities to turn the second half into a stroll.
But they spurned them all before Kennedy’s intervention seven minutes from the end.
Former Celtic striker Watt was denied an 11th-minute opener by a tremendous save from Buddies keeper Craig Samson.
Watt produced a textbook downward header when he connected with Kennedy’s teasing cross, but Samson dropped to his left and somehow scooped the ball up onto his crossbar.
Home goalkeeper Zander Clark required a late intervention to prevent a Lee Hodson cross drifting onto the head of lurking centre Simeon Jackson.
In the 23rd minute Danny Mullen tumbled in the penalty area after a stretching lunge from Murray Davidson, who was among seven bookings.
However, to the dismay of his colleagues referee Andrew Dallas rebuffed their spot-kick pleas and opted instead to caution Mullen for diving when he picked himself up from the turf.
Minutes from half-time Stephen McGinn exploited a Scott Tanser slip only for Mullen to blaze his chance into the stand and at the other end another combination of Samson and the bar prevented a Kennedy header breaking the deadlock.
The Buddies survived a 48th-minute scare when Watt side-footed Tanser’s teasing cross past the post from just six yards with the keeper stranded.
But Wotherspoon slammed home the opener on the hour mark but only after a fruitless swipe from Watt diverted the attention of defenders.
In the space of nine minutes Watt had a 63rd-minute spot-kick stopped by Samson after McGinn barged Davidson over.
Then Craig ballooned his 72nd-minute attempt into the stand when Hodson felled Drey Wright.
But with the Buddies unable to threaten keeper Clark in the second period, the home side wrapped up the points when a Jason Kerr header was palmed aside by keeper Samson and Kennedy tapped home from close range.