Lee Westwood and Ian Poulter each won twice on Saturday at the Seve Trophy as Great Britain and Ireland surged into a 11.5-6.5 lead over Continental Europe.
The defending champions, who led by one overnight, won six points out of eight in the greensomes and foursomes.
They need three points in Sunday's 10 singles matches to retain the trophy for a sixth consecutive time.
"We were really up for it all day, concentrated, focused and got the job done," said captain Paul McGinley.
"I'm still erring on the side of caution, though, because the whole job's not done yet."
Continental Europe had pulled within a point on Friday, but could not compete on Saturday.
In the greensomes, Jamie Donaldson and Simon Dyson beat Nicolas Colsaerts and Matteo Manassero 2&1 to give Britain and Ireland the first point.
Poulter and Ross Fisher then defeated Thomas Bjorn and Raphael Jacquelin 2&1, while Westwood and Scott Jamieson outclassed Miguel Angel Jimenez and Pablo Larrazabal 4&3.
Continental Europe's Peter Hanson and Alexander Noren halved their match with Darren Clarke and David Horsey after Hanson birdied the last hole.
Britain and Ireland made the difference on the back nine. Westwood and Jamieson won six straight holes and were the only pairing leading at the turn while the other three matches were still all square.
In the foursomes, Bjorn and Anders Hansen beat Fisher and Mark Foster 3&2 to secure Continental Europe's only victory on Saturday.
Robert Rock and Donaldson were 1 up before the last hole but Donaldson missed a three-foot putt to split the point with Francesco Molinari and Manassero.
Jacquelin and Colsaerts combined for four bogeys to lose to Westwood and Horsey 4 & 3. Dyson chipped in for eagle on the 17th to earn, with Poulter, a 3 & 1 win over Larrazabal and Noren.