Terry Butcher's side have won their opening three matches, while Kris Commons and James Forrest sealed victory for Neil Lennon's men
The hosts’ performance in the first half did the damage, as Richie Foran struck only four minutes into the match and then Billy McKay added their second nine minutes before the break from David Raven’s pass.
Terry Butcher’s side now have a maximum nine points from their opening three matches and are yet to concede a league goal.
However, they will have to maintain that form if they are to challenge champions Celtic, who maintained their own unbeaten start with a 2-0 win at Aberdeen.
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The hosts kept Neil Lennon’s side at bay for most of the first half, but defender Jamie Langfield was sent off in the 44th minute for fouling Georgios Samaras in the area, and Kris Commons scored from the penalty spot.
Substitute James Forrest then clinched the win three minutes from time.
St Johnstone sit just behind Inverness in second in the table thanks to a 4-0 win over Ross County.
Nigel Hasselbaink and David Wotherspoon gave the home side a 2-0 lead going into the break before Stevie May and Dave Mackay added further goals in the second half.
Meanwhile, Kilmarnock striker Kris Boyd suffered mixed fortunes at St Mirren, as he gave his side the lead in the 49th minute before being sent off 13 minutes later for violent conduct.
Following Boyd’s dismissal, Gary Harkins equalised for the hosts, but they were unable to capitalise on their numerical advantage as it finished 1-1.
There was also a 1-1 draw at Easter Road, where Stuart Armstrong gave visitors Dundee United the lead only for Scott Robertson to equalise for Hibernian with 25 minutes left.
Both sides finished the game with 10 men, though, when Kevin Thomson and Gavin Gunning were sent off for their part in a scuffle.