Alan Judge fired the Bees into an early lead and James Tarkowski put the match beyond the reach of the Royals with a crucial second just after the hour.
Late goals elsewhere meant it wasn't quite the dream afternoon for the west Londoners as Derby salvaged a late point at Wigan and Ipswich beat Nottingham Forest.
However, it gives Brentford hope of making the top six. If Steve McClaren's Rams lose next weekend and the Griffin Park club win then it will be their name in the mix for the end of season lottery.
Brentford’s final game with Wigan next Saturday could be Warburton’s last as manager but he is hoping that the stars will align and he could remain as boss for a Wembley run-out.
“Let's hope so,” Warburton said when asked about the potential of signing off under the arch.
“If you're right there, I'll be buying you a glass of red wine. That's our aim, anyway. It has to be.
"It's very disappointing (to be leaving the club.
"It's a great club, I'm delighted to be associated with it. I've been here four-and-a-half years now. But the situation, it is what it is. I'm sure the club can keep on going forward.
"We weren't at our best today but got an early goal that calmed the nerves and were much better in the second half. The game was too open at times but we got the three points.
"It's tight for those last play-off places so all we can do is focus on the Wigan game."
Brentford lie in seventh place, two points from the top six.
Reading, meanwhile, find themselves limping towards the finish line and have gone eight matches without tasting victory.
Steve Clarke’s team can do the Bees a favour next weekend by taking points off Derby, however the Royals boss knows his side must improve their finishing after drawing another blank.
"We look a good team until we get to the final third of the pitch," manager Clarke said. "That's what's killing us at the moment.
"It's frustrating but, fortunately, we've not got any more home games left. I'm pleased that they're both away.
"We give everybody a game but, unfortunately, the opposition always seem to get more goals than us. That's the reality of the situation.
"The team is in a difficult moment, it seems to be stuck in a bit of a rut. And we're running out of time this season to find a solution."