Paul McGinley and Santiago Luna finished one shot back at 4-under-par 68. Graeme McDowell, Richard Green and Patrik Sjoland followed in a tie for fifth at 3-under-par 69.
Both Tunnicliff and O'Hern completed their rounds before a fierce thunderstorm brought lightning and hail to Gleneagles. Play was halted for nearly three hours before the round resumed at 5:30 p.m. local time.
Tunnicliff, whose lone European Tour victory came at The Great North Open two years ago, picked up his first birdie of the day at the par-5 second and added another at the par-4 seventh.
The Englishman, who is playing with an injured wrist, tallied an eagle at the par-5 ninth and coasted home with a birdie at the par-5 12th to complete a bogey-free round.
'Yesterday I was wondering if I was going to play and didn't hit any balls at all, just rested up so today I went out there certainly relaxed and refreshed,' said Tunnicliff. 'Beware the injured golfer as they say.'
O'Hern played the back side first and quickly made his presence known with back-to-back birdies starting at the par-4 11th. He collected another birdie at the par-3 14th and continued his fine play on the front side with two straight birdies from the second.
The left-handed Australian, who finished fourth last week in Wales, stumbled to a bogey at the par-4 fifth, but recovered with a birdie at the seventh to secure a share of first.
'I do feel like I am continuing on from Wales,' said O'Hern. 'I played lovely golf at the weekend there and I feel that my game is starting to get there. Swing wise it is coming along. It didn't feel right when I first came over this year, but in the last three weeks it is starting to click.'
McGinley, the hero of the 2002 Ryder Cup, also started on the back side with three birdies over his first nine holes. The Irishman added three birdies on the front nine to go a long with a couple of bogeys.
'There was only one dropped shot that I was upset about, on the eighth where I hit a sand-wedge in to the pin which was on the top tier of the green and I tried to get a little bit cute and overshot it,' McGinley said. 'But other than that, it was a really good day.'
Colin Montgomerie finished four shots off the pace in a group at 1-under-par 71 that featured Peter O'Malley and Philip Walton.
Defending champion Soren Kjeldsen struggled with four bogeys and a pair of birdies for an opening-round of 74.