The £26million record signing scored the winning goal from the penalty spot for the second week running.
Tottenham dominated the game, but a killer instinct was lacking at times and Michel Vorm also pulled off a couple of top saves in the Swansea goal.
That killer instinct, of course, would probably have been there had Gareth Bale been here, but the star forward was sunning himself in Marbella instead.
Without him, Tottenham were impressive, but only in patches.
Soldado took his spot-kick well while a pair of bruising performances from Etienne Capoue and Paulinho stifled Swansea's creativity.
Tottenham should have had the chance to bury the game in the first half but referee Neil Swarbrick failed to give what looked to be a clear penalty following a foul by Jonjo Shelvey on Andros Townsend.
Despite having to go through a 4,500-mile round trip to Georgia in midweek, Spurs pressed from the kick-off.
Swansea had little time on the ball, but the hosts had to resort to long-range shots as Ashley Williams kept Soldado quiet.
Paulinho drove in to Vorm's arms from long range and Capoue did the same from a similar angle.
Vorm looked on nervously as Nacer Chadli's wicked free-kick flew a foot over the bar and Spurs then almost grabbed the lead thanks to a mistake from Williams.
The Arsenal target rattled the frame of his own goal with a bullet header and Vorm did well to save the Paulinho's follow-up from close range.
Hugo Lloris had a quiet 25 minutes until the Spurs stopper was called in to action to save from Shelvey at the near post.
It was all Spurs from then on. Paulinho strode past his marker but fired a low shot wastefully wide.
Swansea could only clear Kyle Walker's cross as far as Mousa Dembele, but Vorm pulled off an impressive acrobatic save to deny the Belgian.
When Paulinho stabbed a volley inches wide of a half-open goal, Spurs fans groaned. It seemed nothing was going their way and that sense was only heightened when Swarbrick failed to award a penalty in the final minute of the first half.
Shelvey bodychecked Townsend inside the penalty area, but the referee, after consulting with his flagging assistant, gave a free-kick a yard outside the box instead.
One possibility was that the linesman had flagged for a nudge by Wayne Routledge on Townsend just before he entered the box.
Michael Dawson put in a crucial tackle to deny Michu after the break, but the home side were still well on top.
Townsend cracked a fizzing half-volley just over the bar soon after as Tottenham continued to lay siege to the Swansea box.
The pressure paid off as Tottenham won a penalty in controversial circumstances.
Townsend's trickery allowed him to enter the Swansea box and he fell to the floor after little, if any, contact from Shelvey.
Swarbrick paused before pointing to the spot and Soldado made no mistake, slotting the ball to Vorm's right-hand side to make it 1-0.
Swans boss Michael Laudrup brought on striker Wilfried Bony and the Swans came back in to the match briefly. Pablo Hernandez won a yard of space just outside the box after a weak header from Dawson, but his curling effort flew a yard wide.
Lloris then pulled off a stunning save to stop a powerful volley from Chico Flores.
Andre Villas-Boas brought Sandro on to shore up the Spurs midfield, while Soldado received a big round of applause as he departed for Jermain Defoe.
Paulinho had a chance to kill the game off in injury time, but he ploughed a shot over the bar after first drawing a good save from Vorm.