McIlroy and Hatton were both getting their 2020 Race to Dubai campaigns under way at Chapultepec Golf Club and they both reached three under on a glorious day in Mexico City.
Hatton made three birdies in his first 11 holes, while McIlroy made an eagle and a birdie after starting on the tenth.
American Woodland had three birdies in his first nine holes.
McIlroy - playing his first European Tour event since moving back to the top of the Official World Golf Ranking - finished second at this event last season, while Hatton was third in 2018.
Hatton - a two time Rolex Series champion - was out in the first group of the day and he took on the short par four first, leaving himself ten feet for eagle after driving the green and making an opening birdie.
He made a ten foot birdie putt on the fifth to get to two under and had Billy Horschel for company as the American took advantage of the par five 11th and holed a long putt on the 13th.
Horschel bogeyed the next and was soon replaced in the leading group by McIlroy, who put his second on the 11th to 18 feet and rolled home his eagle putt.
The 30-year-old had another look at eagle on the par five 15th and two putts from 38 feet handed McIlroy the solo lead.
He was not alone for long as playing partner Woodland, who had birdied the 11th and 12th, got up and down from short of the green to move the three under.
Hatton then found the 11th green in two and two putts from 40 feet put him into a share of the lead.
Cabrera Bello sandwiched a birdie on the 11th with bogeys on the tenth and 13th but then holed a 35 footer on the 16th, a 20 footer on the 18th and hit a stunning approach into the first in his first ten holes.
Horschel dropped a shot on the first to slip into a group at one under that also included Thai Jazz Janewattananond, local favourite Abraham Ancer, American Patrick Reed, South African Branden Grace and Austrian Matthias Schwab.