The Tynesiders followed up Saturday's 3-0 win over Chester to leave Southport, who were beaten 3-0 by Dagenham & Redbridge at the weekend, still looking for their first point and goal of the campaign.
The Sandgrounders' best effort came when forward Louis Almond hit the post early on with a deflected effort but, on the stroke of half-time, Danny Johnson broke the deadlock, bearing down on goal before finding the corner.
With four minutes of normal time to go Wes York, who scored twice on Saturday, did well to find an empty net after Ryan Bowman forced goalkeeper Tyrell Belford into a hurried clearance.
Substitute Mitch Brundle lashed home in the last minute to complete the scoring.
Report supplied by the Press Association.
Match ends, Southport 0, Gateshead 3.
Second Half ends, Southport 0, Gateshead 3.
Goal!  Southport 0, Gateshead 3. Mitch Brundle (Gateshead).
Goal!  Southport 0, Gateshead 2. Wes York (Gateshead).
Substitution, Southport. Ashley Grimes replaces Liam Nolan.
Substitution, Gateshead. Mitch Brundle replaces Danny Johnson.
Substitution, Southport. Connor McCarthy replaces James Gray.
Substitution, Southport. John Cofie replaces Louis Almond.
Substitution, Gateshead. Ryan Bowman replaces Reece Styche.
Second Half begins Southport 0, Gateshead 1.
First Half ends, Southport 0, Gateshead 1.
Goal!  Southport 0, Gateshead 1. Danny Johnson (Gateshead).
Liam Hogan (Gateshead) is shown the yellow card for a bad foul.
Neil Ashton (Southport) is shown the yellow card for a bad foul.
First Half begins.
Lineups are announced and players are warming up.
Gateshead made it two 3-0 wins from two matches in the National League this season, beating Southport at Haig Avenue.