The visitors did cross late on through Sinoti Sinoti but it was too little too late and the Italian side headed home still searching for their first RaboDirect PRO12 points.
Laidlaw got Edinburgh on the scoresheet as early as the sixth minute with a fine penalty but the hosts found the going tough in the early stages as Zebre dug deep.
But Edinburgh were patient and the breakthrough did come on 22 minutes as great work from Richie Rees allowed Cox to go through for his second try in as many games, Laidlaw adding the extras.
However just five minutes later Netani Talei was penalised at the breakdown and Daniel Halangahu added the easy penalty to get Zebre off the mark.
And after Laidlaw had restored Edinburgh's ten-point advantage Visser raced over just before half-time to hand the Gunners a comfortable 20-3 lead at the interval.
This had Edinburgh's tails up going in at the break and it took them just three minutes of the second half to extend their lead further.
Ford was the one who got his name on the scoresheet as he powered over on the left wing but all the plaudits went to centre Matt Scott who created the opportunity with a fantastic break through Zebre's midfield.
Fly-half Laidlaw added the conversion and Zebre were soon reduced to 14 men when captain Quintin Geldenhuys was sin-binned for a high tackle on Lee Jones.
Laidlaw was called upon again just before the hour mark, this time adding the extras from a penalty try after Zebre were penalised from the pack.
This woke the Italians up and ten minutes later they had the try their early efforts had warranted as wing Sinoti crossed the whitewash, fly-half Halangahu adding the extras.
There were more worrying signs as Zebre threatened Edinburgh's tryline late on, only for a lack of cutting edge to let the Italian outfit down when it really mattered.
And to rub salt into the wounds Visser scored a great solo effort right at the death, chasing on to his own hack forward to race away to add some extra gloss to the scoreline.
|Edinburgh Rugby Score Card|
|Zebre Score Card|