The home side were second-best throughout the first half but took a 1-0 advantage into the break thanks to a 45th-minute goal by Paul Hanlon. Eoin Doyle added the second six minutes after the restart.
The defeat leaves St Johnstone joint bottom of the division with only one point taken from their opening four games, while Hibs move up into second.
The visitors received a boost before kick-off with the news that Murray Davidson was fit enough to start having shaken off the effects of a knee injury. Gregory Tade and Rowan Vine returned to the line-up after the pair missed last week's 2-1 home defeat to Aberdeen.
Hibs boss Pat Fenlon named an unchanged line-up from the team that defeated St Mirren 2-1 in Paisley last Saturday, which meant that Doyle was preferred to recent signing Shefki Kuqi to partner Leigh Griffiths in attack.
Having taken only one point from their opening three league games St Johnstone started the match with an obvious determination to attack their opponents and leave Easter Road with all three points.
Twice in the opening 15 minutes they may have taken the lead had it not been for the outstretched leg of Hanlon. The centre-back denied first Liam Craig, with a shot from the edge of the box, and then Nigel Hasselbaink after the attacker tried to pass the ball into the far corner from inside the penalty area.
The best chance of the opening half-hour came to Tade. The Frenchman was played through on the left by Davidson, but he failed to get a shot away in time as James McPake was able to get back and block with a lunging tackle.
Hibs had their share of possession in the opening 20 minutes but it was all one-way traffic by the time Vine shot straight into Ben Williams' arms on 35 minutes. Discontent from the Hibs end was barely audible over the roaring encouragement from the small group of travelling support.
The same support were then stunned into silence when their team went 1-0 down on the stroke of half-time. Leigh Griffiths' corner from the right was headed into the ground and over Alan Mannus by Hanlon. Callum Davidson's attempt at an acrobatic clearance could not stop the ball crossing the goal-line and Hibs had an undeserved 1-0 lead.
Buoyed by that goal, Hibs started the second half with a more aggressive outlook and doubled their advantage six minutes in.
Paul Cairney was unfortunate not to be the goalscorer when he wriggled into position for a shot at goal before Steven Anderson's flying block temporarily cleared the danger. Hibs then worked the ball back in the penalty area and Griffiths' cut-back from the left found Doyle free in the six-yard box, and the Irishman finished at the second attempt after Mannus' spectacular save.
St Johnstone should have been back in the match when McPake misjudged a bouncing ball and allowed Tade a free route to goal. The striker had as much time as he needed to pick his spot but saw his shot turned away for a corner by a fingertip save from Williams.
Anderson similarly should have done better with a free header at the back post a few minutes later, and Craig saw a late drive comfortably held by Williams.