There was even better news for QPR as second placed Swansea crashed to a 2-1 defeat at Derby, while fifth-placed Leeds were held to a 0-0 draw by Ipswich and sixth-placed Nottingham Forest drew 0-0 with Doncaster.
Victory over Palace was the perfect end to a traumatic week for the Hoops, who saw their 11-match unbeaten run ended at Millwall on Tuesday and could face a possible points deduction after the Football Association charged them, along with chairman Gianni Paladini, with breaches of regulations relating to third-party ownership and agents.
Warnock was delighted with the way his players ignored the on and off-field issues to focus on getting back on track.
"We've won five out of six matches and that takes some doing given the teams we've played against, so I'm really happy," Warnock said.
"When you've been in the game as long as I have, you don't get carried away when you win games or when you lose them. I said the same after we lost to Millwall in midweek.
"It's not a straightforward job - it never is at QPR and hasn't been this season - but when you get a game and an atmosphere like that, it's all worth it."
At Pride Park, a seventh minute own goal from Ashley Williams set Derby on their way to a first home victory since November and extended promotion-chasing Swansea's winless streak to three games.
Steven Davies doubled the home side's advantage from Conor Doyle's corner in the 54th minute before substitute Darren Pratley got one back for Swansea in the 65th minute.
Swansea boss Brendan Rodgers refused to criticise his players and said: "This group of players are very mentally tough. I trust them 150 percent and I told them I have massive belief in what they do.
"There are still 27 points to play for and it will be what we do in April that will define our season. I think it is going to go to the wire at both ends."
With Forest unable to breakdown Doncaster at the City Ground and Leeds involved in a stalemate with Ipswich at Elland Road, Leicester reignited their promotion challenge with a 3-0 victory at second bottom Scunthorpe.
Hull are another side with the play-offs in their sights after securing a 1-0 victory at Coventry to set a new club record for 14 unbeaten away league matches.
Millwall enjoyed their best away of the season as captain Paul Robinson scored a second-half double to inspire a 3-0 victory against play-off hopefuls Burnley at Turf Moor.
Robinson netted in the 52nd and 71st minutes before on-loan Tottenham midfielder Andros Townsend got the Lions' third goal in the 87th minute.
"It keeps the play-offs open to us and that is an achievement after coming up from League One," Millwall boss Kenny Jackett said.
Sheffield United's chances of avoiding relegation were dealt a further blow as they were beaten 3-0 at Watford after going down to nine men before half-time.
Darius Henderson and Lee Williamson, both former Watford players, were sent off as goals from Danny Graham, Martin Taylor and Ross Jenkins put the Blades to the sword.
Elsewhere, Portsmouth drew 0-0 with Middlesbrough at Fratton Park.
Warnock salutes spirit of leaders QPR
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