Shawn Smith scored 19 to lead the Thundering Herd (2-0) in points. Taylor also led with six assists.
Khaleen Pinkett and Javaris Jenkins each scored 12 for Savannah State (0-2). Jenkins scored on his first shot, putting the Tigers up 2-0, but then Smith nailed a 3-pointer and Taylor added a layup as Marshall surged ahead and didn't look back.
The Herd led by 11 at halftime, and Taylor and Smith rattled off a quick six points when play resumed, prompting Savannah State to call a timeout less than 2 minutes into the half. The Tigers came out of the huddle with a Jenkins 3-pointer, making the score 39-25.
But Marshall continued to score in bunches, from Smith dunks to Taylor 3-pointers, and the lead remained in double digits.