Jones and Nathan Elder each scored a brace for the Bucks and Fleet respectively, but Edwards’ heroics at the death prevented the Telford man from completing his treble.
The result left Andy Sinton’s side 10th in the standings with 23 points from their opening 17 Blue Square Bet Premier matches, while Ebbsfleet remain in the relegation zone with just 15 points.
The game burst into life after just six minutes as Jones stormed into the area to get on the end of Steve Leslie’s cross to guide the ball into the back of the net.
Two minutes later and the visitors were back on level terms, some sloppy defending allowing Joe Howe to get in his delivery which Elder duly headed home.
Chris Sharp was then denied by the goalkeeper while Leslie saw the rebound nipped off his toes, while moments later Sharp’s header was again thwarted by Edwards.
Midway through the first half the hosts regained the lead in sumptuous style as Jones raced onto a ball in behind the defence before lifting chipping the onrushing goalkeeper and into the back of the net.
Shortly after the restart, though, the visitors hit back, Jones turning villain as he brought down Ashley Carew inside the area, with Elder stepping up to slot home the resulting penalty.
Elder then had a great chance to put his side ahead for the first time in the match but could only head over from close range, and deep into injury-time the hosts were gifted the chance to snatch all three points.
The lively Leslie was upended in the area by Patrick Ada, but Jones couldn’t find a way past Edwards while the follow-up from Phil Trainer went wide.