Although the visitors fought back to trail by only one point early in the second half, they were always struggling as the set-piece crumbled.
Worse still, they could pay a heavy price with injuries. They had already lost both of their usual locks during the week and when Ollie Atkins, went off they were forced to play with David Denton, a No 8, in the second row, supported by raw academy products Ben and Alex Toolis.
When flanker Roddy Grant, then hobbled off, centre Andries Strauss had to pack down in his place and the set-piece, already under pressure, fell apart.
"We didn't play well in the first half but made changes and in the second showed a lot of grit," said head coach Alan Solomons. "It was a gritty second half but our injury situation before and during the match made it very difficult for us and our set-piece got hammered. That is the way it is and we have to take it on the chin."
In wet conditions, Zebre eased in front in the opening quarter when they managed to build a rare series of attacking phases on Edinburgh's line and wing Giovanbattista Venditti wriggled his way through the forwards and over for the score.
The home side also won the battle of the boot with three first-half penalties, two from Gonzalo Garcia and one from Luciano Orquera, added to Carl Bezuidenhout's brace.
Edinburgh's changes seemed to re-energise them and they were back in the game when Tim Visser on his return to the starting XV, laid on a score for Matt Scott. With Jack Cuthbert's conversion the deficit was cut to a single point.
It was a false dawn, though. Zebre stretched their advantage again when weak tackling allowed Quintin Geldenhuys, the home captain, almost to the line. His offload to flanker Filippo Cristiano completed the job with the try that put them back in the comfort zone.
Zebre added a third try when they demolished an Edinburgh scum for to allow replacement centre Kameli Ratuvou to cross.