England were leading 13-9 after a first-half Tom Curry try and looked set to make it three wins in a row before the hosts turned the match, and the championship, with a relentless attack that sent Hill over 12 minutes from time.
Winger Adams then caught a high kick in the corner to settle it and send the Principality Stadium into raptures.
Wales top the standings on 12 points, with England second on 10, though, thanks to their earlier bonus points and with home games against Italy and Scotland to come, they are still well-placed to win the title.
France, who beat Scotland 27-10 earlier on Saturday, have six, with the Scots on five. Ireland, on four points, visit bottom side Italy on Sunday.