However, the point will benefit Caley Thistle more than the hosts, moving the third-placed Highlanders closer to a spot in next season’s Europa League.
Both goals arrived in the second half with Aaron Doran firing the visitors ahead on 55 when the Irish striker collected David Raven’s assist before finding the top right-hand corner of the net from 12 yards.
Graham’s leveller eight minutes from time came courtesy of a powerful 10-yard header, following Tam Scobbie’s cross, and Saints must have felt their chances of snatching three points had increased when defender Raven was dismissed on 85 for collecting a second yellow card.
But they were unable to conjure up any meaningful chances during the closing minutes in Perth.
During a goalless first half, Saints came close to opening scoring in the 10th minute when Danny Swanson struck the bar from long range while – seven minutes before the break – Michael O’Halloran fired narrowly over from inside the box.
At the other end, Doran went close for Inverness, with Danny Williams having an effort saved by home keeper Alan Mannus.
Saints then missed a brace of decent opportunities early in the second half, with Swanson and O’Halloran both failing from inside the six yard box before Doran broke the deadlock for Caley.
Inverness, who remain in third spot with a four-point cushion, can also qualify for the Europa League if they beat Falkirk in the Scottish Cup final later this month.