On-loan winger Adam Johnson put Championship leaders Watford ahead but Moore, on as a second-half substitute, may well have kept Gregory in the Loftus Road hot-seat.
Former Chelsea boss Gianluca Vialli and ex-R's player Martin Allen, who have both been linked with Gregory's job, watched from the directors' box as struggling Rangers managed to avoid a fifth consecutive home defeat.
The first half ended goalless despite a frenetic opening in which both sides came close to scoring.
Watford defender Dan Shittu almost netted against his former club but his header from Lee Williamson's corner was pushed onto the bar by keeper Lee Camp.
Williamson and Tommy Smith fired wide of Camp's right-hand post, while Dexter Blackstock had Rangers' best two chances of the first half.
Blackstock did well to jink his way past Jay DeMerit only to slice his shot wide with just keeper Mart Poom to beat.
And, on 28 minutes, he headed Martin Rowlands' left-wing cross wide of the target.
Camp dived to his right to parry Marlon King's 20-yard effort shortly before the break, but he was unable to save Rangers four minutes into the second half.
Smith pounced after Chris Barker's hesitation and pulled the ball back for an unmarked Johnson to score from close range.
But Rangers replied with an equaliser on 59 minutes. Moore crossed for Blackstock whose header struck the bar, and Moore slammed the loose ball into the net from 12 yards.
QPR played the last 10 minutes a man short after Mikele Leigertwood was sent off for a second bookable offence following a foul on Lloyd Doyley.
Watford surged forward but Moore cleared King's shot off the line and Camp produced a fine late save to deny substitute Nathan Ellington.