England's Luke Donald and Paul Casey, who held the lead entering round three, managed a 4-under 68. They stand alone in second place at 23-under-par 193.
The South African team of Trevor Immelman and Rory Sabbatini, who are the defending champions, posted an 8-under 64 to climb into a share of third place at 21-under-par 195. They are joined there by Sweden (Joakim Haeggman & Fredrik Jacobson), Ireland (Padraig Harrington & Paul McGinley) and the United States (Scott Verplank & Bob Tway).
The Spanish duo began the day six strokes behind the Englishmen. Jimenez and Garcia combined to post back-to-back birdies from the third at Real Club de Golf Sevilla to get to minus-15.
An eagle at the par-5 fifth by Garcia moved the Spaniards to minus-17 and within three shots of the English lead.
The Spanish team got rolling again with a birdie at the par-5 ninth. They came right back with a birdie on 10 and made it three straight at the 11th. That moved them to 20 under par and within two strokes of the lead.
The Spaniards kept their charge going with a birdie at the 13th. They briefly joined England atop the leaderboard with a birdie at the 14th. However, England birdied the 13th two groups behind the Spanish team to reclaim the lead at 23 under.
Garcia's second eagle of the round, from 6 feet out at 16, jumped the Spanish team to minus-11 for the day and 24 under par overall, which gave them the outright lead for the first time in the round. They parred the final two holes to remain one clear of the field.
'We are definitely pleased with the result,' said Garcia. 'We made a couple of big putts and we gelled very well. When I was out of a hole Miguel was right in the thick of it and when he was a bit out, I was in. That was important. The support of the crowd helps us. The crowds have been unbelievable.'
England's lead grew quickly to six strokes when they birdied the first hole. As other teams began to close in on them, they picked up another birdie at the fourth that got them to 21 under and padded their lead to four strokes.
A birdie at the ninth moved England to minus-22, but Spain and the United States got within one shot with a Spanish birdie at 13 and an American eagle at the same hole.
The Englishmen birdied the par-5 13th to regain the outright lead for the final time in the round. They could only par the final five holes to close one stroke behind the Spaniards.
'Obviously it was frustrating for us today,' Donald said. 'Fortunately we had a lead to work with and although we've lost it, we are still very much in the hunt. If we play like we did in the foursomes we can still win it.'
The Japanese team of Shigeki Maruyama and Hidemichi Tanaka posted a 7- under 65 to move to 20-under-par 196, where they stand alone in seventh.
The Dutch duo of Robert-Jan Derksen and Maarten Lafeber fired a 9-under 63 to jump to 19-under-par 197. They share eighth place with the Australian pair of Stephen Leaney and Nick O'Hern, who posted a 65.
Austria's Martin Wiegele and Markus Brier, who gained entry into the event when the team from Thailand withdrew, carded a 68. They are joined in 10th place at 18-under-par 198 by the Welsh pairing of Bradley Dredge and Phillip Price, who posted an 8-under 64.