The Imps tested Dan Hanford early on through Elliott Whitehouse, but Gateshead held firm and found themselves in front on the half-hour mark after Luke Hannant was brought down in the box by Sean Raggett.
Paddy McLaughlin coolly slotted home the resulting penalty, sending Paul Farman the wrong way, and the hosts held on to their lead after Hanford pulled off a superb finger-tip save to deny a Nathan Arnold volley just before the break.
Matt Rhead equalised for the league leaders from the spot in the first minute of stoppage time, before Arnold fired in the winner two minutes later.
Match report supplied by Press Association.
Match ends, Gateshead 1, Lincoln City 2.
Second Half ends, Gateshead 1, Lincoln City 2.
Wes York (Gateshead) is shown the yellow card.
Goal!  Gateshead 1, Lincoln City 2. Nathan Arnold (Lincoln City).
Goal!  Gateshead 1, Lincoln City 1. Matt Rhead (Lincoln City) converts the penalty with a.
Substitution, Gateshead. Mitch Brundle replaces JJ O'Donnell.
JJ O'Donnell (Gateshead) is shown the yellow card.
Liam Hogan (Gateshead) is shown the yellow card.
Substitution, Lincoln City. Josh Ginnelly replaces Harry Anderson.
Substitution, Lincoln City. Adam Marriott replaces Lee Angol.
Second Half begins Gateshead 1, Lincoln City 0.
First Half ends, Gateshead 1, Lincoln City 0.
Goal!  Gateshead 1, Lincoln City 0. Patrick McLaughlin (Gateshead) converts the penalty with a.
Sean Raggett (Lincoln City) is shown the yellow card.
First Half begins.
Lineups are announced and players are warming up.
National League promotion-chasing Lincoln came from behind with two goals in the last three minutes as they stunned Gateshead 2-1.