Canizares also birdied three straight from the 14th and was one shot ahead of Thailand's Kiradech Aphibarnrat and Australia's Marcus Fraser.
Stenson said he felt no ill effects from an injured right wrist that restricted his practice to nine holes this week on the Earth Course at Jumeriah Estates.
Rose trails Stenson by $287,033, with the winner in Dubai earning $1.3 million. The Englishman mixed three birdies with a bogey on the 17th, and saved par at the 18th with a 20-foot putt.
In Playa del Carmen, Mexico, Brian Stuard topped the OHL Classic lederboard at 5 under with three holes left when first-round play was suspended for the day because of rain and wet conditions.
More than 3 inches of rain soaked the Mayakoba Resort since early Wednesday night.
In Guadalajara, Mexico, Thailand's Pornanong Phatlum took the first-round lead in the Lorena Ochoa Invitational, birdieing seven of the first 13 holes at Guadalajara Country Club.
The 23-year-old Phatlum, winless in five seasons on the LPGA Tour, dropped a stroke on the par-4 14th hole and finished with a 6-under 66.
Amy Yang was a stroke back, and fellow South Korean players Inbee Park and So Yeon Ryu were two shots back at 68 along with Sweden's Anna Nordqvist.