The Eagles trailed 21-18 at halftime and 37-31 after three quarters, but outscored the Warriors 18-6 in the fourth to pull out the win and advance to the next round. Davis scored 10 of his points in the final period, while Jones had 14 of his points in the second half.
Zac Anderson paced Lakeview with 18 points, while Kane Smith added eight.
In other action from Monday, the second-seeded Ringgold girls coasted to a 40-16 win over Chattanooga Valley behind 13 points from Dare Schley and 10 points from Karoline Sholl.
Amaya Harrington and Haley Sandridge had four points each for the Lady Eagles.
The Trion Lady Bulldogs failed to score in the fourth quarter, but still managed to hang on for a 22-19 win over Rossville in the final game of the night.
Jordan Thrasher had 11 points for Trion. Mary Curtis and Desiree Russell had five and four points, respectively, for Rossville.
Play will begin again on Tuesday with the top-seeded Gordon Lee boys facing Chattanooga Valley at 4:30 p.m., followed by the top-seeded Heritage girls against Trion.