Will Jenkins and Aaron Martin's second-half goals helped South Shields to a fourth consecutive win in the Vanarama National League North.
Paul Blackett opened the scoring in the 36th minute after his penalty deflected off Banbury goalkeeper James Dadge.
Aaron Martin scored with his first touch in the 75th minute not long after Will Jenkins had doubled the Mariners' lead.
Shields came into the game fresh from victory in Chester courtesy of a late Paul Blackett goal.
Banbury hadn't picked up a point since early February prior to this game and winless under new manager Kevin Wilson.
Elliott Dickman made no changes to the side that beat Chester, but Jordan Hunter was named on the bench to mark his first squad involvement since King's Lynn.
Banbury were without goalkeeper Jack Harding after picking up an injury away to Curzon Ashton, James Dadge made his debut in between the sticks for the Puritans
Shields suffered an early blow 10 minutes into the game as Dillon Morse was caught on his ankle and forced off for Jordan Hunter
After a period of chances for the Puritans, Paul Blackett was brought down in the box in the 35th minute to which the Mariners were awarded a penalty.
Blackett stepped up to take the spot-kick which ricocheted off the post and hit Puritans goalkeeper James Dadge and into the net.
Will Jenkins provided Shields' second of the game in the 52nd minute picking up the ball in the Banbury box and striking it home from close range to claim his third goal since his return from Morpeth.
Banbury had a handful of chances that seemed to fizzle out, including an audacious effort from Emmanuel Maja to catch Myles Boney off his line but the Shields shot-stopper was able to calmly collect.
The best chance the home side would get came in the 70th minute when a combination of Boney and Tom Broadbent managed to block shots from Banbury at full stretch.
Aaron Martin came on as a second-half substitute replacing Paul Blackett in the 75th minute and had the ball in the back of the net with his first touch courtesy of a sublime cross from Jenkins to make it 3-0 to Shields.
As the game went on, the Puritans would apply pressure to the Shields defence but no chances ever seemed to trouble the Mariners.
A 94th-minute corner for the hosts saw a half-volley go wide and that would be the final chance for either side.
The result puts Elliott Dickman's side in sixth and into the play-off places.
Banbury are now nine points adrift from safety.
South Shields: Boney, Clarke (Abbey 73), Morse (Hunter 14), Broadbent, Adams (C), Briggs, Smith, Jenkins, Heaney, Stephenson, Blackett (Martin 75)
Unused subs: Savage, Seymour
Goals: Blackett (36'), Jenkins (52'), Martin (75')