The Spaniard coolly converted from 12 yards in the 37th minute after Ryan Shawcross had handled an Emmanuel Adebayor volley.
Soldado failed to convert several other chances from open play, but it mattered little as Tottenham made the game safe after the interval to secure a first home win under Tim Sherwood.
Mousa Dembele doubled the hosts' lead in the 65th minute as he sent a low shot into the bottom corner from 20 yards, and four minutes later Aaron Lennon volleyed home a third.
The win moves Tottenham up to seventh place in the Premier League table, while Stoke - who mustered just one effort on target - are 12th after a second heavy defeat in succession.
Paulinho returned from suspension and Lennon made his comeback following injury as Sherwood made five changes to Tottenham's side.
Stoke manager Mark Hughes called on Andy Wilkinson and Wilson Palacios to replace the suspended Glenn Whelan and Marc Wilson, who were sent off in a 5-1 loss at Newcastle United on Thursday.
Defender Ezekiel Fryers, making his first Premier League start for Tottenham, appeared fortunate not to be penalised as his side's last man early on when Jonathan Walters went to ground.
Aside from that incident, the hosts were much the stronger side in the first half and saw each of their strikers come close after 15 minutes.
After Stoke had a penalty claim following a challenge from Michael Dawson on Oussama Assaidi waved away, Soldado broke the deadlock.
Shawcross was penalised for blocking a goalbound volley from Adebayor with his arm, and Soldado made no mistake from the spot when sending Thomas Sorensen the wrong way.
Stoke substitute Charlie Adam sent a free-kick wide after the break, yet it was Tottenham who remained the more dangerous.
Soldado missed another chance before his side's lead was doubled in the 65th minute through Dembele.
The Belgium international was given far too much time on the edge of the penalty area, and worked an opening before firing low across Sorensen and into the bottom-right corner for his first league goal of the campaign.
Four minutes later Tottenham’s victory was secured as Lennon registered his first goal in 21 games.
Adebayor failed to connect with a cross from Soldado, but the ball ran to Lennon, who volleyed confidently past Sorensen after the ball had sat up invitingly.
Peter Crouch had Stoke's only attempt on target when he met a late cross from Jermaine Pennant, but the striker's tame header was comfortably saved by Hugo Lloris.
