The striker slotted in his spot-kick in the second half before Ross Draper was given his marching orders for the visitors.
And the Saints will feel it was a deserved victory after creating the better chances in the game.
Their best opportunities in the first half fell to Michael O’Halloran, who blazed his first effort over early on.
The Saints striker then found himself through on goal but his effort from 12 yards was blocked by Caley goalkeeper Dean Brill with his chest.
Inverness’ best chance came through Aaron Doran, whose shot towards goal from 20 yards was deflected just wide of the target.
The Saints improved after the break and broke the deadlock on the hour mark when Graham was brought down in the box by Brill and converted the penalty.
Caley’s hopes of salvaging something from the game took a further blow when Draper was shown a straight red in the 67th minute for hauling down Simon Lappin.
St Johnstone dominated the rest of the game with David Wotherspoon’s shot from a tight angle was tipped over by Brill.
And one goal was enough to seal victory and keep them in sixth place in the Premiership table, while Caley slip to fourth position.