A Josh Walker brace helped Gateshead stretch their unbeaten run at home to five matches against Salisbury.
Gateshead broke the deadlock after just 50 seconds from Walker's 12-yard strike before James Marwood doubled the lead just moments into the second half.
Walker headed a second not long after but Salisbury pressed late on after Jamie White's header pulled one back.
Elliott Frear further cut the deficit when he coolly slotted home but the hosts held on to seal all three points.
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Gateshead manager Gary Mills told BBC Newcastle:
"We were dominant and excellent in going 3-0 up and I thought there was some great football, but then we created a problem for ourselves.
"If we want to go anywhere we have got to cut that out, and improve in that side of the game.
"We have to know when a game has to be killed and know when to go forwards.
"The players are learning. I'm not saying we're perfect, but we are doing all right and overall, they have been superb since I came in."
Salisbury City manager Mikey Harris told BBC Wiltshire:
"I'm bitterly disappointed with the goals we've conceded. To concede in the first minute of the game is unforgivable and then to do it again in the second-half, I'm absolutely fuming.
"We came here with a game plan. I don't think we did what we've been working on all week as well as we should have done.
"We've got to take our medicine, we've got to react from this.
"We nearly got a point but we didn't so now it's time to move on."
Gateshead 01 Bartlett 16 Baxter 22 Sirrell 06 Clark 05 Curtis 17 Walker 18 Marwood (Ramshaw - 89' ) 04 Chandler (Magnay - 84' ) 08 Turnbull 29 Oster 07 Larkin Substitutes 15 Tait 14 Brown 02 Magnay 21 Ramshaw 12 Boyes Salisbury City 01 Puddy Booked 06 Wilson (MacDonald - 79' ) 16 Dutton 05 Clarke 07 McPhee 08 Wellard (White - 66' ) 11 Frear 14 Sinclair Booked 15 Wright (Thomson - 9' Booked ) 10 Lewis 20 Fitchett Substitutes 17 Feeney 25 Bittner 21 Thomson 23 MacDonald 09 White