Substitute Adam Coombes struck in stoppage-time to stretch Paul Doswell's side’s winless home league run to seven matches.
But despite a much-improved second-half showing from the hosts, substitute Coombes’ effort two minutes into injury-time extended Hawks run without a home league win.
Hawks made two changes from the side who drew at Billericay on Saturday with Paul Rooney returning from a three-match suspension and Tommy Wright coming in for starts in place of Jamie Collins and Guy Hollis.
Joint leading scorer Wright partnered forward Jake Andrews in a makeshift central midfield highlighting Hawks’ current injury issues.
The hosts looked disjointed in the first-half, failing to create any clear-cut openings, as neither goalkeeper was tested in an underwhelming opening 45 minutes.
Ross Worner was out quickly to thwart Joseph Turner inside three minutes while Tommy Wood and Tom Beere sent efforts flashing wide for Tonbridge.
While Jonathan Henly in the visitors’ goal was virtually untroubled as Hawks were carrying very little threat going forward.
The hosts came out full of life after the restart, going close when Josh Passley's deflected cross flashed across the area on 55 minutes.
But the breakthrough arrived from the resulting corner, with captain Oastler attacking the ball from Andrews' corner and heading home from close range.
Hawks had plenty of attacking fluency after the break and Andrews should have doubled the advantage on 63 minutes, yet he fired straight at Henley having latched onto Scott Rendell's clever flick.
Tonbridge so nearly levelled with 11 minutes of normal time remaining but Worner saved brilliantly from Turner’s strike just inside the area after some sloppy Hawks defending.
Just as Hawks were on course to pick up a much-needed three points on home turf, substitute Coombes waltzed in unmarked at the back post to slot past Worner and snatch a point for the visitors.
Hawks: Worner; Rooney; Bailey, Oastler, Gobern, Passley, Andrews, Wright, Newton, Rendell, Wall. Subs: McCarthy (Wall, 45), Jewitt-White (Andrews, 74), Roberts (Bailey, 74), Read, Searle.