The visitors were the better team in the first half and Jonny Hayes hit the post after a mazy run.
But the Perth side picked up after the break and were unlucky not to win a penalty for Roman Golobart's barge on Fran Sandaza.
However, Dundee United's defeat at Aberdeen allowed the Saints to leapfrog them in the race for a European place.
St Johnstone manager Steve Lomas made one change to the side that lost 2-0 to Celtic last weekend.
Frazer Wright was suspended and Steven Anderson returned in central defence. There was still no place for new signing Derek Riordan in the squad.
Inverness manager Terry Butcher also made a solitary change following last Sunday's 3-2 home defeat to Hibernian.
Striker Gregory Tade dropped to the bench and Owain Tudur Jones came into the side.
St Johnstone were desperate for a win to stay in pursuit of Dundee United and Motherwell in the race for European football.
Caley Thistle are well clear of relegation trouble but Butcher was keen for a morale-boosting display ahead of the split.
Hayes scored a spectacular, if fortunate, effort against Hibs last weekend and almost repeated the trick in the opening minutes.
His cross was whipped in above Alan Mannus but landed on the top of the net as the Saints goalkeeper breathed a sigh of relief.
Hayes looked in the mood and was inches away from opening the scoring in 10 minutes.
He surged down the right wing, left three defenders trailing and curled a wonderful effort off the post.
Inverness were dominant and Richie Foran's long-range drive was saved superbly by Mannus. Josh Meekings also came close for the Highlanders.
St Johnstone finally settled and Golobart was booked for a foul on Cillian Sheridan.
Dave Mackay curled the resultant free-kick narrowly wide. Sandaza was also unlucky with a near-post flick.
Foran's powerful header was saved by Mannus as Inverness continued to cause problems.
However, Sandaza was starting to exert his influence and teed up Liam Craig for a low drive that flew wide.
St Johnstone suffered a setback when Lee Croft limped off with a hamstring injury in 35 minutes. Kevin Moon replaced him.
The home side looked more like themselves after the break and had a strong penalty claim turned down.
Sandaza was sent crashing to the ground by Golobart when trying to round Tuffey but referee Kevin Clancy waved play on.
Lomas could not hide his anger and was given a warning by the referee after taking his complaints too far.
Sandaza was also left shocked by the decision but could have made up for it when he met Sheridan's cutback - but his shot was weak.
St Johnstone continued to press and substitute Marcus Haber wasted a good chance after being sent free on the left.
Inverness enjoyed a rare attack and Richie Foran fell under Jody Morris' challenge, but there was no real contact.
Sandaza missed a close-range header and Meekings wasted a chance for Caley as both sides settled for a draw.
