Will Middleton put Ealing ahead at 8-7 only for Mate Nyaka to equalise. There were just 13 seconds remaining when ex-Sheffield player Tom Kelly claimed the winner.
Cambridge chalked up their second win, beating York City 8-6 thanks to goals in the last three minutes by Riccardo di Pietro and Nick Ludford.
In Championship 2 at Matlock, Exeter beat Watford 13-11 with late goals by Kameron Powell (2) and Andy Barry while a dominant third period, which they won 6-1, earned Sutton & Cheam a second victory - 19-16 against Hucknall.