Dundee went on the attack straight from the kick-off and Bryn Halliwell had to be on his toes early to save Derek Lyle's right-foot drive.
With seven minutes on the clock Lyle was shown a straight red card for an off the ball incident as both sets of players waited for a Dundee free-kick.
Jason Scotland thought he had given the visitors the lead on 12 minutes but his header was chalked off for a foul.
St Johnstone did take the lead on 27 minutes when Paul Sheerin volleyed Andy Lawrie's cross past Ludovic Roy from eight yards.
Kevin McDonald's cross cum shot low to the near post was blocked by Halliwell before Paul Dixon saw his 30-yard effort fly just over as half time approached.
Early in the second half McLaren headed wide and moments later gaffer Alex Rae shot high and wide from 20 yards.
Steve Milne should have doubled the visitors' lead on 53 minutes but a great save by Roy denied him.
McLaren went close again on 66 minutes when his shot on the turn from 12 yards was saved by Halliwell.
Ten-man Dundee grabbed a deserved leveller on 71 minutes when McLaren blasted home from six yards after great play down the left by Gavin Swankie.
With just five minutes left, and all their substitutes used, Dundee went down to nine men when Ross Harris was carried off just eight minutes after coming on, but the hosts held on to earn a fine point.