The Blades, who knew they needed victory to avoid the drop, endured a terrible start as goals from Noel Hunt and Hal Robson-Kanu put the Royals 2-0 up after 20 minutes, but Adams' men did not give up and Darius Henderson netted a double either side of Lee Williamson's strike to secure a 3-2 win.
Adams, whose side remain six points from safety with two games remaining, said: "The way the game started it could have been embarrassing. We started nervously and didn't look as if we thought we could win, but we ended up worthy winners.
"Goals change games and when Henderson got the first goal our tails were up. I'm just pleased to win an away game. I've not experienced an away victory since I've been at the club and I was proud of the players.
"Staying in the Championship still looks nigh-on impossible, but what we have got to do is win against Barnsley next week.
"If we don't win then goal difference will not make any difference and I don't think they'll help us because of the revenue from a local derby."
Source: PA
Source: PA