The Scot, whose best result this season is a tie for 53rd, came home in 31 after also picking up shots at the 12th and 13th to sign for a six-under-par 66.
“I’m delighted with that start,” said three-time European Tour winner Warren. “I finished with three birdies in a row so it kind of makes it look a little bit better obviously. Overall, it was really solid tee to green.
“I putted really well today, my pace was really good. The putts that missed I didn’t leave myself much to do and the good putts always looked like they had a chance of going in.”
Dunne, who recorded a top-10 spot in the Houston Open last month, also finished strongly, with three birdies and an eagle on the 18th in a back nine of 31.
“I find the greens quite tricky to read, especially on the front nine, so it was nice to get a couple of putts to go in on the back nine and climb up the leaderboard,” said the British Masters champion.
World No 4 Jon Rahm surprised himself with an opening 67 after fearing he’d have little left in the tank following his joint fourth place behind Patrick Reed in the Masters.
“It feels great,” said the Spaniard, who carded an eagle, four birdies and a solitary bogey at the Centro Nacional de Golf, where he practised as an amateur.
“To be honest I would have taken anything under par given the fact that I played better than I expected, especially off the tee. My long game was amazing.”
Asked how he was feeling after his Atlantic crossing, Rahm added: “The morning is not as bad as the afternoon. When jet-lag kicks in after the round and adrenaline goes, the afternoon is a little harder. I’m a lot better than I expected and hopefully it keeps going because sometimes jet-lag tricks you. It gives you a good day and the next day is horrible.”
Scott Jamieson fared next best among the Scots with a 69, followed by Stephen Gallacher and Connor Syme with matching 70s.
Meanwhile, Scotland have been drawn in the same group as Ireland, Italy and France for next month’s GolfSixes at the Centurion Club near St Albans. Richie Ramsay, who claimed third spot in last year’s inaugural event alongside Warren, is partnered by Jamieson.
A ‘Captains Team’ featuring Catriona Matthew and Thomas Bjorn are in Group B with Australia, South Korea and Spain.