Stokes fired Hibs ahead against the run of play with an opportunist strike from 18 yards.
Derek Riordan doubled the lead before half-time with a long-range drive and Stokes curled home a free-kick to remove any doubt about the destiny of the points.
St Johnstone manager Derek McInnes no doubt looked on with envy at such deadly finishing as his players missed numerous chances.
The victory got Hibernian's season back on track following a defeat by Hamilton that sparked John Hughes into three changes.
Stokes' former Sunderland team-mate, Liam Miller, made his first start and youngsters Darren McCormack and David Wotherspoon returned with Chris Hogg and Patrick Cregg dropped and Colin Nish suspended.
Saints were missing the influential Felipe Morais but their five-man midfield - which featured the recalled Chris Millar, Liam Craig and Martin Hardie - helped create enough chances to win the game in the opening 10 minutes.
Murray Davidson headed over Dave Mackay's cross and Hardie lashed a volley against the bar after the ball fell kindly for him 16 yards out.
Lone striker Collin Samuel just missed Craig's low cross and the same pair linked up for the clearest opportunity of all with the midfielder unable to guide his free header from eight yards underneath the crossbar.
Samuel could also have made more of two clumsy penalty-box challenges from Sol Bamba before Stokes benefited from some route-one football in the 21st minute.
The 21-year-old chested down Bamba's hopeful long ball on the edge of the box, held off Graham Gartland before turning and firing a left-foot shot into the bottom corner. Wotherspoon volleyed just wide from 22 yards as Hibs belatedly took control in midfield, and Riordan doubled their lead in the 36th minute with another goal out of the blue. Wotherspoon's blocked cross fell for the former Celtic striker 22 yards out and he rifled the ball into the bottom corner.
Graham Stack saved well from Craig's long-range strike but Saints struggled to get back into the game until McInnes changed his tactics in the 57th minute with the introduction of strikers Kenny Deuchar and Steven Milne for Samuel and Craig.
Davidson was foiled as he attempted to force home a long throw before Stokes missed a chance to put the game beyond Saints when he blazed over from 14 yards after Stuart McCaffrey had misjudged Wotherspoon's cross.
The action was now moving quickly from end to end - Stack was well positioned to save Milne's overhead kick before Wotherspoon fired over from a tight angle.
Deuchar volleyed well over from 10 yards after Davidson's header found him unmarked, and Hardie curled a 20-yard free-kick just off target.
Danny Galbraith replaced Riordan and the former Manchester United youngster quickly made his mark by winning the free-kick that allowed Stokes to bag his second in the 73rd minute.
The winger's positive run was crudely halted by Gartland and Stokes curled home from 22 yards with Alan Main motionless.
Hibs had a let-off when Ian Murray appeared to clear Deuchar's header from behind the goal line following a long throw, and the striker then sliced high and wide from a tight angle after beating Stack to a long ball.
McCaffrey headed over from substitute Gavin Swankie's corner as Saints kept going forward without reward.