Brentford cruised to victory in this First Round Replay albeit after a shaky start.
But two goals directly before the break effectively decided the tie and the second half could easily have seen the Bees reach double figures.
It was the non league visitors who settled first and forced two corners within the first two minutes following an early effort which Lewis Price parried wide of the post.
But Brentford responded with a determined run from Cleveland Taylor down the right flank which led to a through ball for Marcus Bean which he chipped just wide of the left hand woodwork.
After 15 minutes a good turn by Ben Strevens saw the ball run through for Charlie MacDonald whose effort was blocked for the hosts first corner of the game. A minute later Phil Turnbull played on to Graeme Armstrong who was only denied a chance on goal by a saving tackle from Danny Foster.
A Leon Legge back header flew not too far wide of the woodwork with Price backpedalling in the 34th minute. Then two minutes on a fine run by Taylor was thwarted by a defender on the edge of the area.
But the deadlock was broken in the 42nd minute with MacDonald taking the ball in the area but he slipped as he looked to take a chance on goal only for the ball to find itself at the foot of Strevens who lashed it high into the top of the net from 12 yards out for his first goal for the Club.
Just three minutes on and a long ball down the flank by Foster found the on running Taylor whose resultant centre was headed text book style into the back of the net by MacDonald.
Six minutes after the break a dazzling run by Taylor saw him beat three players before his diagonal centre was tapped home by Strevens. However he was flagged for being offside.
Six minutes on and the arrears were halved when Armstrong lashed the ball home wide of Price from 15 yards out.
But the Bees soon extended their lead again when two minutes on Marcus Bean, who had taken control of the ball in his own half, threaded the perfect ball forward to MacDonald who toe poked the ball home from the edge of the area.
A further eight minutes on and Myles Weston unleashed a spectacular effort from fully forty yards out which flew high into the corner of the net.
The Bees completed their nap hand in the 74th minute when Weston was on hand to fire home after a MacDonald effort had been blocked inside the area.
Gateshead notched a second with nine minutes remaining when Armstrong scored a duplicate of his first goal.
The Bees now have the pleasure of hosting Walsall on two consecutive Saturdays in the League and FA Cup.
Bees: Price, Foster, Legge, Osborne, Dickson, Taylor, O'Connor, Bean (Hunt 78), Weston, Strevens (Cort 71), MacDonald
Unused Subs: Moore, Bennett, Kabba, Wood, Blake.
Attendance: 1,960 (Gateshead fans: 112)