The four-times major winner's four-under-par effort left him two strokes behind leader Alex Noren of Sweden.
McIlroy, who began his round at the 10th hole, started off with a bogey six but recovered in style with three birdies on his outward half including a brilliant four at the 18th that came after he drove his ball into the water off the tee.
He had three more birdies on his inward nine, mixed in with a bogey five at the second hole.
"It wasn't the best way to start... but to bounce back and birdie some of the tougher holes on the course, I was really pleased with that," the 26-year-old Northern Irishman told reporters.
"When I got myself out of position I was able to get back in play."
There has been something of a question mark raised about McIlroy's form on the greens in recent times but he said it was now going in the right direction.
"I still feel there's room for improvement in my putting but it's definitely got better," he added.
"Ever since winning this tournament back in 2009, the strides I’ve made in my putting have been great. I feel like I’ve got a consistent routine in practise and that definitely helps on the course."
McIlroy's victory in the Desert Classic seven years ago was his first win as a professional.
Triple champion Ernie Els of South Africa also carded a first-round 68, as did British trio Chris Wood, Graeme Storm and Simon Dyson, Spain's Alvaro Quiros, American David Lipsky and Bernd Wiesberger of Austria.
In second place on 67 were Spain's Rafael Cabrera-Bello, Brett Rumford of Australia, South African Trevor Fisher and Peter Hanson of Sweden.
(Writing by Tony Jimenez, editing by Pritha Sarkar)
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