Iain Vigurs snatched the opener for County 17 minutes from time in a 90 minutes largely dominated by the hosts.
Matty Kennedy had earlier headed over from a yard for Saints and also hit the bar with a powerful drive on the hour mark.
And the winger was involved when the Perth side earned a valuable point six minutes from time as they stretched their unbeaten run to five matches.
His cross was nodded in by Hendry before County's Brian Graham was red-carded for a second booking in injury-time.
St Johnstone came into the match eager to maintain a revival that has now seen them lose just twice in their last 10 matches.
The Saints dominated the opening half but without creating anything clear-cut in front of goal.
Ali McCann, scorer of the winner against Hamilton Accies on Boxing Day, had one shot blocked before the County defence stood firm to repel a Matty Kennedy effort.
For all the home team's stranglehold on possession, County always knew they only needed one opportunity.
They carved out one in the 21st minute when Ross Stewart engineered some space at the edge of the area with a one-two but his drilled effort was too straight to trouble Zander Clark in the St Johnstone goal.
County came closer to a breakthrough 12 minutes later courtesy of a mistake from Saints skipper Jason Kerr.
The defender took a fresh-air swipe at an excellent Josh Mullin cross but the error surprised substitute Graham, just on for the injured Stewart, and he could not capitalise as he took a heavy touch six yards out.
The second period kicked off with St Johsntone again enjoying the upper hand.
McCann showed a greater determination with a run that climaxed with a curling shot that slipped by the far post.
Then Kennedy was guilty of a stunning miss. Drey Wright's free-kick was nodded back by Kerr but the winger got under his header and sent his effort over the bar from point-blank range.
Eager to make amends, the attacker swung a free-kick just too high before coming closest to the breakthrough on the hour mark.
Pouncing when Harry Paton gave away possession, the wide man drove forward and drilled in a shot from 25 yards out that Nathan Baxter touched onto the crossbar.
But it was the Staggies who finally found the opening goal in the 73rd minute.
Blair Spittal's looping cross from the left was headed back by Mullin and Billy Mckay held the ball up long enough for Vigurs to drive his shot in off the right-hand post.
However, Saints snatched a deserved point when Kennedy's cross from the left was fired home by Hendry from six yards out.