The capital side were slow into their stride, seemed to go off the boil once the victory was in the bag and coughed up a soft and undeserved try to their Italian opponents in the last few minutes.
Yet, given their side's terrible RaboDirect PRO12 form last season, those fans should not be too dogged in resisting the urge to celebrate. With all allowances made and asterisks applied, this was still a comfortable win, Edinburgh's second in three games, and a useful workout for those players who had been rested against Cardiff last weekend.
Michael Bradley could find reasons for satisfaction beyond the numbers that lit up the scoreboard at the finish. "Obviously, we're very happy with the five championship points," the coach said. "The boys worked hard in the first half and Zebre did as we expected, defending well and making it difficult for us. But we were patient, and clinical when we had the opportunities. The same goes for the second half. We took a couple of chances, but we lost our rhythm a little bit after the fourth try."
The Edinburgh pack were aggressive in their hunt for the ball throughout and there was another conspicuously effective performance by Sean Cox in the second row. Grant Gilchrist, his lock partner, also put in an energetic shift, but there still seemed to be a lot of rustiness about aspects of their performance. That said, Edinburgh have unquestionably strengthened the depth of their squad, and Bradley can turn to his bench without anxiety.
After their team's stirring win at Cardiff, there was an almost palpable expectation among the home crowd in the minutes before the match. Zebre, however, had welcomed back a handful of first-choice players who had been missing from the sides that had lost to Dragons and Connacht over the previous two weekends, and right from the off they looked a pretty stuffy outfit.
The Italians weren't exactly glistening with creativity, and toiled against an Edinburgh scrum that is starting to build a formidable reputation, but they kept the Scots well clear of the danger area throughout the first quarter.
The three points Edinburgh did harvest in that period came from a fifth-minute penalty kicked by Greig Laidlaw from fully 45 metres out.
Laidlaw attempted a dropped goal 10 minutes later, only for the effort to be charged down by Tito Tebaldi, the Italy scrum-half.
Until then, there had not been so much as a sniff of a try from the home side, whose back-line alignment seemed off at times. Greig Tonks and Nick de Luca produced a couple of eye-catching solo runs, but collectively things just weren't quite there.
Unsurprisingly, then, the breakthrough score came from another piece of individual brilliance. This time it was dished up by Richie Rees, the scrum-half, who broke from behind a ruck in the 22nd minute, scuttled past a couple of attempted tackles, then drew the full-back before offloading perfectly for Cox to finish the job. Laidlaw clipped over the conversion and Edinburgh were 10-0 ahead.
An exchange of penalties followed soon after, but Bradley's side were clearly growing in confidence. And already thinking about bonus points, it seemed, with two more penalty chances turned down in favour of kicks to the corner.
From one, in the 38th minute, Zebre won a scrum, but Edinburgh turned them over, spun the ball left to produce what is fast becoming an almost inevitable feature of their PRO12 games: a try by Tim Visser, his fifth of the season.
After that score, it was probably no coincidence that Christian Gajan, the Zebre coach, made three changes to his underpowered pack at half-time. Already, though, Edinburgh's focus was moving away from the scrum, and they opened the second half with a brilliant, scything run by Matt Scott.
The centre's burst of elusive pace took play from halfway to the right corner, from where Edinburgh launched the second wave to send Ross Ford over for a try, albeit one that involved some rather guddled handling along the way.
The reward for Ford, and the two starting props, was to be retired from the fray a few minutes later. Not that Edinburgh were noticeably weakened by the changes. Just short of the hour mark they crushed the Zebre pack, diminished by the yellow-carding of Quintin Geldenhuys, in three consecutive scrums. When the third set-piece collapsed the referee had no option to award the penalty try that gave Bradley's men their bonus point.
Edinburgh eased off, perhaps disrupted by their own raft of substitutions, and they were dozing when they allowed Sinoti Sinoti to nip in for Zebre's try in the 69th minute. It would have been a travesty for those to be the game's final points, and Visser put things right with a break-away try in the last minute.