"I was just happy to get the drive off the tee on the first and that was all that mattered. I hit a good shot into three and I think that settled the nerves.
"When we started, I heard a lot of shouts like 'come on Tom' but I suspect they might have been for the other Tom, not me. But towards the end I thought, maybe there were a few for me - it would be nice to think so anyway."
Meanwhile, late arrival Bjorn earlier joined the Open Championship party in style with a brilliant 65.
The, sixth reserve last week and who only found out he was playing on Monday night following Vijay Singh's through injury, made the most of his late call up with a five under round on the course where he suffered Open heartbreak eight years ago.
Bjorn, who until this week had not set foot on the course since blowing a three shot lead with four holes to play in 2003, exacted a measure of revenge with seven birdies in a sparkling round including three on the spin from 14.
That included a birdie on 16 where he famously took three to get out of the bunker to let the Claret Jug slip from his grasp into the grateful hands of Ben Curtis.
But Bjorn was not dwelling on his past travails at the testing Sandwich links.
"A lot of people have asked me about what I feel about the 2003 Open. It's in the past," he said.