Pittsburgh had suffered two setbacks in a row before producing a dozen hits that lifted them to a 7-1 advantage heading into the ninth.
The Pirates put their first five batters on base in the second and had six hits in the inning while scoring three times. It was still a 3-0 contest when Jones hit his home run in the sixth, his fifth of the season. Jones has had at least 20 home runs in three of his last four campaigns.
Wandy Rodriguez (3-2) gave up a run on six hits in six innings to collect the victory. After the Mets had scored twice in the ninth and had two men on with two away, Jason Grilli was called on to record the final out and pick up his 14th save.
Shaun Marcum (0-3) was charged with the loss after surrendering six runs on nine hits in 4 2/3.