Hodgson converted a Darius Osei cross three minutes after captain Robert Briggs had equalised for the Mariners as they got the better of their National League North opponents with a 2-1 win.
Former Newcastle United youngster Adam Campbell had fired Gateshead into a first half lead but Shields displayed impressive poise to claim the win with their two goals just after the midway point of the second half.
The hosts – lining up in a 5-3-2 formation – started brightly and created an early opportunity as Conor Tee manouevred his way into a crossing position on the left and delivered the ball onto the head of Alex Kempster, whose effort was saved by Jacob Chapman.
They fell behind in the 10th minute, though, as Gateshead pressed high to win possession and Cedwyn Scott squared to Adam Campbell, who rifled home from 12 yards.
Graham Fenton will have been delighted with the way his side responded to the opening goal.
Nathan Lowe proved a thorn in Gateshead’s side and his effort from distance was parried by Chapman to begin a period of pressure from the hosts as they probed for an equaliser.
Lowe’s free-kick less than a minute later dropped to the feet of Alex Kempster, who had a shot deflected wide, while Dillon Morse’s header from the resulting corner was blocked.
Jon Shaw thought he had levelled moments later as he headed home against his former club, but the offside flag denied the player-joint assistant manager.
Shields were left scratching their heads as to how they failed to level the scores on 16 minutes when Chapman brilliantly kept out Shaw’s header from a Lowe corner and the rebound was powered towards goal by the head of Morse but cleared off the line by Macaulay Langstaff.
The Heed weathered the storm and went in search of a sucker punch at the other end, which they twice went close to delivering.
First Greg Olley picked out Ryan Wombwell with a teasing free-kick from the left, but the defender could only hook the ball over from an inviting position at the back post.
The away side then went closer as Olley slid in Langstaff and his low strike was destined to find the bottom of the net before Shaw raced back to block superbly.
A strong appeal for a Shields penalty was waved away 12 minutes before half-time when Massanka and Jordan Hunter combined down the right and the latter’s cross was arrowing towards the head of substitute Robert Briggs, who appeared to be bundled over. The referee waved play on and Blair Adams sent the loose ball over the bar.
Massanka, Hunter and Shaw were all denied by blocks as the first half ticked into stoppage time but the Mariners were sent into the interval with a harsh one-goal deficit.
Shields created a decent chance for an equaliser in the 56th minute when Adams fired a dangerous ball across the area from the left. It arrived quickly at Massanka, though, and he was unable to turn it home.
Myles Boney kept the deficit at one with an excellent save as the game ticked onto the hour mark.
Scott was released down the left of the box for the visitors and his powerful low effort appeared certain to double his side’s lead, but Boney spread himself well to superbly deny him with his outstretched left foot.
Langstaff slid a low shot past the post in Gateshead’s next attack after linking up with Bailey, but the introduction of Lowe and Sam Hodgson proved pivotal for the Mariners midway through the second half.
First Hodgson forced a corner with some tireless running and then Lowe took full advantage of it, drilling a superb free-kick into the near post area which Briggs met with a powerful header that Chapman was unable to keep out.
Shields completed a three-minute turnaround as the four-figure crowd played their part by notching up the noise.
Darius Osei motored in down the left of the area and fired an excellent ball across the box which Hodgson sent flying into the roof of the net.
The Mariners were playing with supreme confidence and had opportunities to seal a fine win, with Chapman saving well from Osei at the near post from a Lowe free-kick before denying the same player moments later after some terrific pressing presented him with a one-on-one chance.
The failure to force a third goal did not cost Shields, though, as they saw out the remaining minutes to defeat Mike Williamson’s side.
They now have a week to prepare for their opening Pitching In Northern Premier League match against Mickleover at 1st Cloud Arena on Saturday.
South Shields: Boney, Hunter (Jenkins 77) Adams (c) (Kempster 77), Shaw (Morse 67), Morse (Trialist 46), Trialist (Bodenham 25), Kempster (Osei 32), Ross (Lowe 67), Massanka (Hodgson 67), Lowe (Tee 46), Tee (Briggs 25). Subs not used: Steavens, Agnew, McGowan, Rossiter.
Goals: Briggs (71), Hodgson (74).
Attendance: 1,148 (139 Gateshead).