Wales won the Triple Crown at Twickenham after the substitute Scott Williams scored a stunning breakaway try to thwart a battling England.
Farrell, the fly-half, once again displaying an ice-cool temperament, kicked four penalties to Halfpenny's three before going off injured 15 minutes from time.
A final twist seemed possible when the England wing David Strettle came close to scoring a try as the game headed into added time.
He was tackled by the Wales centre Jonathan Davies, yet players and fans were subjected to a nerve-shredding delay of around four minutes before Iain Ramage, a Scot and the television match official, ruled that Strettle had not got the ball down.
Toby Flood, on for Farrell, was lined up to attempt a potential match-levelling conversion when the referee Steve Walsh relayed Ramage's verdict and blew for full time.
The glory, though, belonged to Williams, whose 50-metre breakaway try came when he robbed the England lock Courtney Lawes of possession, sprinted away and then gathered his kick to score, giving Wales only their second Twickenham triumph since 1988.
"It is quite unbelievable really," Williams said. "Our defence was superb. We stuck in there and managed to get the win."
He said a turning point was keeping England at bay while Rhys Priestland was off with a yellow card.
"England put us under pressure, but we soaked it up until it was time for him to come back on," Williams said. In many ways, it was rough justice on England after they pushed below-par Wales to the limit, but they lacked a killer instinct.
England could still win the Six Nations title, yet Wales clearly now have the advantage, with the title and Grand Slam theirs if they win home games against Italy and France next month.
Sam Warburton, the Wales captain, was both exasperated and relieved.
"We didn't play well at all and we knew it was going to be the toughest game of the Six Nations," he said.
"We didn't pay attention to anything in the media in the build-up … "To win in Triple Crown at Twickenham is amazing but we can't look any further than one match ahead."
Should they win out, it would give them the second Six Nations title and Grand Slam of Warren Gatland's four-year tenure as coach, but France in Cardiff on March 17 will provide a huge obstacle to overcome.