Lewis hit a 3-pointer with 2:06 left in overtime to give the Vikings a 60-55 lead. Green Bay was scoreless in the extra period until Keifer Sykes hit a pair of free throws with 59 seconds left that cut the deficit to three.
Lewis and Green Bay's Greg Mays quickly traded baskets, and Cleveland State (17-11, 11-3 Horizon) hit its last four free throws to secure the win.
Anton Grady had 20 points and 11 rebounds for the Vikings, who moved alone into second place in the league, a game ahead of Green Bay (21-7, 10-4). Charlie Lee added 12 points, five rebounds and six assists.
Mays had 19 points, seven rebounds and four blocks and Sykes scored 18 for the Phoenix.