Replacement Vosawai grabbed the crucial converted try on the stroke of half time and prop Rizzo put daylight between the two sides when he dived over for another seven-point score on the hour mark.
Edinburgh searched for a response but despite a numerical advantage in the closing stages it was Treviso who had the final say when Favaro sealed the win.
Edinburgh lost the reverse fixture 27-22 in October but enjoyed a fine start when Greig Laidlaw struck a long-penalty through the posts for the lead on three minutes.
The Italians could have levelled the match two minutes later but from his shot at goal Alberto Di Bernardo was off target.
Undeterred, Treviso continued to press, throwing the ball around in attack but Edinburgh scrambled well to keep them out and ruffled the home side's feathers when Netani Talei forced full-back Brendan Williams to knock on.
Edinburgh's pressure paid off on 13 minutes when they moved the ball along the back three to Scotland wing Tim Visser who made good yards before putting international team-mate Scott through for the game's first try. Laidlaw continued where he had left off with the boot and added the extras.
Di Bernardo was again afforded the chance to produce an instant response but once more he failed to secure the three points.
Treviso continued to attack and despite dogged defence from the Scottish side they eventually had an infringement punished when Di Bernardo kicked his first successful penalty.
The Italians were given further encouragement when Brown was sent to the sin bin seven minutes before the break and Di Bernardo slotted another penalty.
Treviso sensed blood and finally found the try they were looking for when Vosawai dived over after a pick and go from the scrum and Di Bernardo converted on 40 minutes.
Scott almost began the second half with a bang for Edinburgh, chipping the ball over the defence but just failing to collect it.
Brown returned to restore Edinburgh to full strength but Treviso continued to attack with ambition
The Italians then demonstrated their power up front but after winning the penalty Di Bernardo's effort cannoned back off the upright.
Edinburgh's defence was undergoing a severe examination and after they were penalised at the breakdown Di Bernardo made no mistake.
On 58 minutes 16-10 became 23-10 when a strong maul took Treviso into the Edinburgh 22 before they span out and Rizzo dived over before Di Bernardo converted.
Edinburgh were given a chance when Edoardo Gori and Ignacio Fernandez Rouyet were both sin-binned in the final ten minutes but instead it was Treviso who grabbed their third try of the game through Favaro and Di Bernardo converted.
|Benetton Treviso Score Card|
|Alberto di Bernardo||3||3||15|
|Edinburgh Rugby Score Card|