The Welshman teed up Jan Vertonghen for Spurs' opener in the seventh minute, before brilliantly rifling home his 27th of the season for club and country to double the lead.
Michu got his 20th of the campaign after the break to set up a frantic final 20 minutes, but Andre Villas-Boas' side held out to get their Champions League push firmly back on track after back-to-back defeats against Liverpool and Fulham.
Swansea have now lost their last three since reaching the 40-point mark with victory over Newcastle, but Michael Laudrup's men will feel they deserved a point after a rousing fightback.
There have been an endless stream of plaudits directed at Bale during his remarkable run of current form, and observers were once again attempting to come up with appropriate superlatives as he gave Tottenham an advantage they were not to surrender.
The Wales international, who scored here for his country in midweek, produced a sublime lofted pass to catch Dwight Tiendalli out of position and play in Vertonghen.
The Belgium brilliantly brought the ball down and slotted beyond the advancing Michel Vorm to give the visitors the lead.
Swansea should have been two goals down just six minutes later. Moussa Dembele put Emmanuel Adebayor through for the Togo striker to comfortably outpace Ashley Williams, only to fire tamely at Vorm.
But the lead was doubled in the 21st minute courtesy of a supreme finish from Bale.
Vertonghen found the forward on the edge of the Swansea box, where he took one touch before dispatching an unstoppable strike past a statuesque Vorm.
Swansea were stunned and began to exert their first real spell of pressure, with Nathan Dyer and Tiendalli getting away shots on goal.
Dyer missed a gilt-edged chance on 35 minutes. The winger was picked out by Tiendalli but smashed his header against the bar from just four yards.
Michu also headed wide from another excellent Tiendalli centre as Swansea targeted full-back Kyle Naughton, but Spurs reached half-time with their two-goal advantage intact.
Swansea enjoyed further pressure after the interval and Brad Friedel, playing due to Hugo Lloris' knee injury, had to be alert to deny Michu after Wayne Routledge had fed him from a quick free-kick.
Their attacking ambitions left the hosts stretched at the back and former Swan Gylfi Sigurdsson drew a sharp stop from Vorm with a wicked dipping strike.
Michu then wasted another excellent opportunity as he headed wide from the sort of chance he has made a habit of taking during his first season in English football.
The Spaniard's frustration boiled over as he was booked after clattering Scott Parker as they contested a header.
But he gave the Swans hope as he found the net for the first time since the Capital One Cup final on 70 minutes.
Substitute Ki Sung-yueng delivered a superb corner, and Michu made no mistake as he directed a header in off the far post.
Bale raced up the other end, taunting and teasing the Swansea defence, before rolling a shot against the outside of the post, but it was brief respite for Spurs.
Michu and Vertonghen were involved in an unseemly scuffle, but when the action resumed Dyer blasted over and Bale brilliantly denied his former Southampton team-mate with a superb block.
Temperatures were raised on both benches after Spurs fitness coach Jose Mario Rocha tried to prevent Swansea taking a quick throw.
Words were exchanged between Rocha, Steffan Freund and Swansea's Alan Curtis and Oscar Garcia as play continued, although the situation was eventually diffused as Spurs held out for a valuable victory.