Newton first made landfall Tuesday morning at the southern tip of Mexico's Baja California peninsula.
The tourist destination of Los Cabos was drenched with heavy rains, and rainfall accumulations were estimated at 8 to 12 inches over parts of Baja California Sur and 5 to 10 inches across northwest Mexico, according to The Weather Channel.
Newton could remain a Category 1 or be downgraded to a tropical storm when it likely makes landfall again after midnight Tuesday.
"There are only minor damages — fallen branches, some fallen banners, some cables. ... In general, no victims," Mexican Army Col. Enrique Rangel told The Associated Press.
As it moves north, the storm could drop 1 to 3 inches of rain over parts of Arizona and New Mexico through Thursday, threatening flash floods and landslides, forecasters said.
Despite Newton becoming only the seventh hurricane since 1971 to make landfall near Los Cabos, the damage has paled in comparison to Hurricane Odile, which decimated parts of the popular beach resort in September 2014.
Meanwhile, Florida continued to clean up after being struck by Hurricane Hermine last week, a storm that has since become a post-tropical cyclone.
The system weakened but lingered as it churned in the Atlantic Ocean on Tuesday, and forecasters said it could continue to affect coastal areas of southern New England with high surf and dangerous riptides until Thursday.
The National Weather Service at midday Tuesday discontinued the tropical storm warning associated with the Hermine, which was about 150 miles southwest of Nantucket, Massachusetts, and moving west at 3 mph.
Florida still had thousands of utility customers without electricity more than four days after Hermine slammed into the state as a Category 1 on Friday — the first hurricane to make landfall there since 2005.
State officials said Tuesday that more than 16,000 of those customers reside in Leon County, which is home to the state capital of Tallahassee.
Heavy winds felled trees and power lines throughout the state, and Gov. Rick Scott has called on private companies to help the utilities restore electricity.