And he was again called on to lead from the front, this time for his country with Warburton starting on the bench.
Tries from fellow Lion Alex Cuthbert and Scott Williams had helped them to a 17-3 half-time lead.
But the Italians responded with Michele Campagnaro crossing twice but Wales, who had another Lion Leigh Halfpenny kick 13 points, took the 23-15 victory.
And while not the convincing result many were hoping for, Jones insists their mistakes were borne out of their ambition to play more open rugby.
"I don't think relief is the word, I think it was a good test for us to start with," said Jones.
"It probably looked worse than it actually felt on the park.
"A willingness to play with ambition comes with mistakes. Ultimately we started to come back into the game but we couldn't keep the tempo up, particularly at set-piece time for certain reasons.
"We were looking to play and use the ball - thing we've been criticised on in the past - with that comes mistakes but we got the win.
"But we need to hold on to the ball when we get into those attacking areas.
"In the past we've seemed to get more points the more phases we go through and we really don't want to put ourselves under pressure at those times."