Neither side managed to find a cutting edge at Tulloch Caledonian Stadium but both goalkeepers performed important saves to deny their opposition. The draw moves St Johnstone above Ross County into fourth place, while Caley Thistle remain third - closing the gap on second-placed Motherwell to two points.
With top-six football secure for both sides prior to this game, it was case of seeing how high they can finish. However, this was the third draw between the teams this season.
Newcastle loanee Mehdi Abeid almost made an immediate impact for the visitors, flashing a shot across the face of goal in the second minute. Owain Tudur Jones and Billy McKay had chances as Inverness responded well.
Chris Millar sent a shot off target for Saints, before Tudur Jones forced a terrific full-stretch diving save from visiting goalkeeper Alan Mannus. Inverness keeper Antonio Reguero was next to be called into action when he saved from Rowan Vine.
Reguero also thwarted an attack from Liam Craig on the half-hour mark and Abeid sent a long-range effort close. Abeid continued to look threatening after the restart with a shot from distance stopped by Reguero.
Graeme Shinnie ballooned an effort over the bar for the hosts after Welsh international Tudur Jones' 25-yard shot was parried out by Mannus. The goalkeeper was on hand again moments later when he denied Aaron Doran when the Irishman was through on goal.
Inverness continued the momentum, carving out a chance for Andrew Shinnie, but the Scottish international sent it wide. Vine had the ball in the net for St Johnstone 19 minutes from the end but referee Kevin Clancy ruled it out due to a foul on Josh Meekings in the build-up.
Saints substitute Nigel Hasselbaink came close seconds after entering the fray with 10 minutes to go but his goalbound effort hit team-mate Frazer Wright on the line.
Ross Draper might have made the breakthrough in the 85th minute when his header connected with a long crossfield pass from Nick Ross - but Mannus managed to parry the ball to safety. Abeid tried his luck from 30 yards again in the final minute but failed to hit the target, as the game ended goalless.