The match ignited with three late first-half goals, the first coming in the 35th minute as Jack Parkinson curled in superbly off the post for the visitors from Mitch Pinnock's corner.
Gateshead broke away to equalise straight from kick-off when Wes York was on hand to tap in after Jones' point-blank shot was saved.
Jones then collected Paddy McLaughlin's cross superbly to put the hosts in front in the 44th minute.
McLaughlin made it 3-1 three minutes into the second half, but Ricky Miller halved the deficit after 57 minutes with his 10th goal of the season.
Sam Jones fired his second past Mitch Walker two minutes later to restore the two-goal lead but missed out on a hat-trick when he hit the crossbar with a penalty.
Report supplied by the Press Association.
Match ends, Gateshead 4, Dover Athletic 2.
Second Half ends, Gateshead 4, Dover Athletic 2.
Substitution, Dover Athletic. Sammy Moore replaces Chris Kinnear.
Mitch Brundle (Gateshead) is shown the yellow card for a bad foul.
Substitution, Gateshead. Gus Mafuta replaces Nyal Bell.
Substitution, Gateshead. Reece Styche replaces Wes York.
Wes York (Gateshead) is shown the yellow card for a bad foul.
Aswad Thomas (Dover Athletic) is shown the yellow card for a bad foul.
Ricky Miller (Dover Athletic) is shown the yellow card for a bad foul.
Goal!  Gateshead 4, Dover Athletic 2. Sam Jones (Gateshead).
Goal!  Gateshead 3, Dover Athletic 2. Ricky Miller (Dover Athletic).
Goal!  Gateshead 3, Dover Athletic 1. Patrick McLaughlin (Gateshead).
Second Half begins Gateshead 2, Dover Athletic 1.
First Half ends, Gateshead 2, Dover Athletic 1.
Goal!  Gateshead 2, Dover Athletic 1. Sam Jones (Gateshead).
Goal!  Gateshead 1, Dover Athletic 1. Wes York (Gateshead).
Goal!  Gateshead 0, Dover Athletic 1. Jack Parkinson (Dover Athletic).
First Half begins.
Lineups are announced and players are warming up.
Sam Jones hit a brace as Gateshead beat Dover at the International Stadium.