However, an inspired kicking display by Luciano Orquera nearly saw the Italians wrench away any kind of result away from Jones' men - until Jevon Groves touched down for a converted try in the dying stages.
Edinburgh are now next up in four days' time and with the two sides neck-and-neck in the RaboDirect PRO12 table, Jones believes his side's display bodes well for their chances.
"We are heading into the game against Edinburgh in much better shape and I am very pleased about that," Jones told the South West Argus.
"I was delighted to the response to what happened against Connacht. Okay, we didn't get the win that we wanted against Zebre but we got the performance in lots of respects.
"We looked ten times better than we did against Connacht and the way that they players managed the week of build-up to the game was really good."
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Guinness PRO12 Dragons News
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