Under the guidance of Spanish Olympian Iker Martínez and expert navigator Andrew Cape, Telefónica scythed 11 miles off the pacesetters in the past 12 hours.
"Right now we're just going fast compared to yesterday," Cape said. "There are some long miles to clear the land, and some long miles before the West Indies, so there's a lot of sailing to do. We're going to turn up the heat and win the race."
Telefónica, who top the overall standings by 16 points, have been playing catch-up after their plan to position themselves east of the fleet failed to pay off and they were left in fourth place just ahead of Groupama sailing team.
Since then Telefónica have overhauled Abu Dhabi Ocean Racing to jump up to third and at 1300 UTC on Friday they were the fastest boat in the fleet, trailing second-placed CAMPER with Emirates Team New Zealand by 13 miles.
Cape, who has seen his team to three offshore leg wins so far, said the crew were confident of a comeback.
"There may still be a drag race in those sort of conditions we're pretty good," he added. "There's a long way to go, and we can do it."
The same could not be said for French team Groupama who have struggled to find their feet, now 104 miles behind PUMA with little chance of making up ground in the immediate future.
"We're not in the position in the fleet that we'd like to be in," Groupama bowman Brad Marsh said. "We've had a tough 48 hours trying to work out what the wind is going to do."
Despite their current deficit, Marsh said the leg was far from decided with more than 3,500 miles left to sail to the finish in Miami.
"We've fallen back behind the fleet a little bit but there's still lots more chances to catch up on this leg," he added. "The fat lady hasn't sung just yet, and I don't think she knows what song she's going to sing.
"We'll just keep pushing away, try to stay as close as possible to the boats in front and hopefully get an opportunity to catch up."
Although into the favourable and more consistent trade winds, the teams have not seen the blistering speeds they had hoped for due to the effects of a low pressure system in the South Atlantic.
Once past Recife on the northeast tip of Brazil, expected to happen tomorrow, speeds will increase as the wind strength intensifies.
On second-placed CAMPER, the crew's focus was directed fully at whittling down PUMA's lead.
"We're set up pretty nicely so hopefully we can make some gains on PUMA," helmsman Tony Rae said. "They're going to get round the corner of Brazil ahead of us but hopefully we can chip away and drag them back in."
The current ETA for the leading boat into Miami is May 8.