Melton were put into bat by visitors Hinckley Amateur and made a solid start.
Opening pair Gary Potter and Ben Redwood both made half-centuries and put on 77 runs for the first wicket.
Several other players made contributions to get Melton to 202 and maximum batting points.
Hinckley began with a 50-run partnership followed by a century stand, leaving the visitors needing just 50 runs from 18 overs for victory.
But wickets then started to tumble, and the scoreboard transformed from 155-2 to 158-4, and then 165-5.
Hinckley managed to hold their nerve against the pressure, building a 33-run partnership before Melton’s bowlers unleashed another devastating attack, taking four wickets for four runs in as many overs.
But Melton had left themselves with too much to do, and Hinckley grabbed the winning runs in an exciting finale.
Melton: G. Potter 53, B. Redwood 64, P. Stevenson 9, J. Taylor 24, L. Freer 4, P. James 27, S. Handley 1, M. Hurrell 7*, K. Tew 1, W. Holt 2, H. Gibbs 1, Extras 9. Total: 202.
Bowling: K. Tew 12-5-37-3; P. James 8-2-37-1; J. Taylor 11-1-61-2; J. Culy 4-1-24-0; B. Redwood 7.3-1-28-2.