The Heed controlled the game early on but struggled to make their dominance pay as Patrick McLaughlin and Danny Johnson spurned good chances.
Reece Thompson punished them for not taking advantage just after the half-hour mark, nipping in front to poke home Taron Hare’s fierce delivery from the left.
James Bolton hit the bar with a header and Gateshead camped in the hosts’ half for long periods after the break, but it was to no avail as North Ferriby climbed one place to 23rd.
Guiseley salvaged a 1-1 draw against Chester to boost their National League survival hopes at Nethermoor Park.
James Alabi broke the deadlock in spectacular fashion for Chester with an overhead kick in the 29th minute, smashing home from Blaine Hudson’s flick-on.
Simon Walton equalised for the hosts from the penalty spot after 52 minutes, sending Alex Lynch the wrong way after Johnny Hunt brought down Connor Brown in the box.
The draw extends Chester’s unbeaten run to six matches and they are up to seventh in the table, while Guiseley remain 22nd.
Tranmere climbed to the National League summit, but needed a last-gasp goal to beat strugglers York at Prenton Park.
James Norwood powered in a header at the back post deep into injury time to break the Minstermen’s hearts.
The visitors threatened to turn up the books from the outset, Rhys Murphy warming the gloves of Scott Davies from distance.
Tranmere found it hard to assert themselves, though Kyle Letheren also had to be alert to turn aside a Norwood header.
York also threatened after the break when debutant Jon Parkin attempted to lob Davies, but the stopper back-pedalled excellently to tip over.
Despite York’s positive efforts, they extended their dismal sequence to 18 matches without a win.