St Johnstone captain Dave Mackay put the hosts in front with a neat finish five minutes into the second half at McDiarmid Park, but Craig diverted Iain Vigurs' shot into his own net 20 minutes from time.
St Johnstone created the first chance of the game on three minutes when Tade failed to connect properly with Nigel Hasselbaink's cross and put it harmlessly wide. Anderson then headed over from Craig's free-kick.
Stuart Kettlewell tried his luck on 11 minutes with a shot from outside the area after Vigurs' initial close-range shot had been blocked by home goalkeeper Alan Mannus.
Craig linked well with Tade down the left on 15 minutes, but County defender Grant Munro swept the ball clear in the box before the home striker could connect.
Visiting captain Richard Brittain volleyed wide of the left-hand post on 25 minutes after his side did well to retain possession in the box, while moments later Craig came equally close at the other end, heading off target at close range from Callum Davidson's pass.
The best effort of a goalless first half came just before the break when MacLean unleashed a rising shot from outside the box which Michael Fraser had to stretch to tip over the bar.
St Johnstone took the lead five minutes into the second half when Mackay met MacLean's pass and cut inside Marc Fitzpatrick on the right side of the box and tucked a neat finish in at the near post.
The hosts almost doubled their lead two minutes later when Tade cut inside on the left and linked well with MacLean, but his shot was blocked on the line.
Brittain then deceived the home defence with a quick free-kick to Vigurs on the left of the box, and his shot deflected in at the near post off the outstretched leg of Craig as he attempted to clear.
Tade was prevented from putting St Johnstone back in front just three minutes later by a crucial tackle from substitute Ross Tokely, while Mackay took a 30-yard free-kick 10 minutes from time which went straight into Fraser's arms.
Vigurs tried to find a stoppage-time winner for County with a speculative shot from outside the box, but it went over.