Beautiful Fenway Park is 102.
.
And Red Sox management has done some upgrades, and is committed to be at Fenway for the foreseeable future. Fenway Park and Wrigley Field are the only major league parks I know which were 100 years old and still in use, and not slated to be replaced anytime soon.
Think Wrigley Field is at 100 years old this year.
The 3rd oldest ball park in MLB is Dodger Stadium at Chaves
Ravine in LA. It is 55 years old.