Westwood made six birdies and an eagle in the warmup event before next week's British Open. A bogey at the 16th hole was his only setback.
With a win at the new links course at Castle Stuart, the second-ranked Westwood would regain the No. 1 ranking held by fellow Englishman Luke Donald.
Tullo, ranked No. 232 and in his first season on the European Tour, birdied his first four holes and then five of the back nine to join Westwood atop the leaderboard.
"I like playing the week before a major because I like being competitive and the aggression of making putts when you have to make them," Westwood said. "The more pressure I'm under this week the better, I think."
Westwood and Tullo took advantage of the better conditions in the morning, with a moderate wind picking up slightly in the afternoon. Of the leading five players, only Olesen teed off after midday.
Among those at 5-under 67 were Donald, defending champion Edoardo Molinari of Italy and former Ryder Cup captain Colin Montgomerie, who needs a top-five finish to have a chance at the one available qualifying spot for the British Open for the leading nonexempt player.
"It's a tournament I've loved -- and finished second in -- and I want to play again in it, I really do," Montgomerie said of his attempt to make his 22nd straight Open.
Sixth-ranked Phil Mickelson posted a 1-over 73, leaving the American an uphill task to end his tournament drought in Britain. Graeme McDowell, the 2010 U.S. Open winner, and three-time major winner Padraig Harrington both shot 69s in the afternoon.
Westwood hasn't finished outside the top 11 in his last five events -- including the Masters and U.S. Open -- and he continued his superb form with a near-flawless round starting on the back nine.
He added to an early birdie with a burst of birdie-eagle-birdie around the turn, before a chance meeting with Manchester United manager Alex Ferguson -- who was in the crowd watching his home tournament -- moments after going 6 under at the 12th. Westwood picked up two more shots over the next three holes before his only bogey.
His eagle came after a second shot within four feet of the pin at the 607-yard 18th hole.
"When I play well, I'm in contention now. When I don't play well, it seems to be that I still finish in the top 20," Westwood said.
Donald, playing with Montgomerie, was at par after 10 holes but a run of five birdies in his closing eight lifted him up the leaderboard.
"Tee to green, I was pretty solid, and I caught fire a little bit on my last nine holes. It was nice to finish as strong as I did. I stayed patient," Donald said.
Mickelson went 2 under with a birdie on the 10th but his trademark short game let him down on the 14th, where he made a double bogey.
"That derailed the round. It was a great day for scoring and I thought the course played terrific. I played reasonably well but I was disappointed with the way I scored," said Mickelson, who is already eight shots off the pace.