Rebels defender Damian Webber and Bishop's goalkeeper Richard Day were sent off in separate incidents before half-time and six other players were booked in an eventful game.
Webber saw red for two bookable offences and Day, son of former West Ham keeper Mervyn Day, followed for handling outside the area.
Former Arsenal striker Martin Hayes, Bishop's player/manager, took over as stand-in goalkeeper but was replaced by Carl Fannon in the second half when Worthing struggled to impose themselves.
Rebels goalkeeper Lee Bray made important saves from Hurracia Willock, Hayes and Trevor Paul before Funnell seized on a through ball from Mark Burt to hit the late winner from the edge of the area.
Worthing, who had an early penalty appeal waved away when Lee Weston appeared to be impeded, went behind on 15 minutes through a free kick by Tony Leary but Adie Miles levelled five minutes later with a cross shot following good work by Funnell.
Vinny John cashed in on a mistake by Bray on 24 minutes to restore the visitors' lead and Webber was dismissed following a challenge with John.
But the match changed before the break as Day was sent off as he came out of his area to challenge Funnell. The former Albion striker promptly made it 2- 2 direct from the free-kick.
Bognor's misery in front of goal continues as they went down 3-1 at home to promotion-pushing Grays Athletic.
Assistant manager Neil Hider believes his side is suffering a confidence crisis. He said: "You can see the lack of confidence."
Rocks got off to a fine start when Clinton More headed home a Dean Blake corner on his debut in the eighth minute.
And Bognor goalkeeper Colin Matthewswas in sparkling form when Grays threatened.
But the visitors equalised in the 47th minute when Bognor hesitancy allowed Jamie Riley to finish off a fine solo goal by rounding Matthews and slotting home.
David Wright should have regained the lead for Bognor within minute but shot wide from close in.
Scott Bundy then rifled a volley straight at Ian Brooks, before Jamie Howell broke the offside trap brefore shooting strasight at the goalkeeper.
Grays defender Mark Riley headed home a free-kick five minutes from time before Steven Dickinson ensured the visitors maintained their promotion push when he rifled home a Donovan Wilson corner deep into injury time.
Rocks assistant manager Neil Hider said: "The game hinged on three major incidents, our defence should have dispatched the ball into row Z for their first goal, David Wright should at least have hit the target, and Jamie Howell chose the wrong option when clear through."
Horsham made it two victories out of three under new boss John Maggs with a vital 2-1 Division Two success at Molesey.
Hornets stay third bottom but have now closed the gap to one point with two games in hand.
Maggs believes his side have what it takes to avoid the relegation trap door. He said: "We battled hard against Molesey and if we show that level of commitment in our remaining games then we'll be OK."
Excellent
Hornets were two goals up inside ten minutes through Steve Flain and Martin Lempriere.
The home side reduced the deficit just after the break, also from the penalty spot.
Lewes overcame Hertford 3-1 at home in Division Three despite having a much changed side due to illness, injuries and suspension.
They got off to an excellent start when after five minutes a slick pass from Jack Dineen found Simon Chapman who calmly slid the ball passed keeper Lee Bozier.
Rooks doubled their lead on 28 minutesthrough Gareth Batty.
Lewes wrapped up the game two minutes into the second half when Tommy Pattenden rose to head home a Batty corner.
Chris O'Brien reduced the deficit nine minutes from time.
Converted for the new archive on 30 June 2000. Some images and formatting may have been lost in the conversion.
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