Roberto Martinez's men led in the 15th minute thanks to Kevin Mirallas picking out the top corner in superb style.
However, Everton's advantage was short-lived as Christian Eriksen, scorer of Tottenham's last-gasp winner against Hull City last weekend, converted the rebound when Tim Howard saved from the impressive Harry Kane.
Eriksen has established himself as a crowd favourite since joining in August last year - something that cannot be said for Spain international striker Soldado, who signed in the same month but has found goals incredibly hard to come by.
But the 29-year-old striker offered a decisive glimpse of the form that made him so highly sought-after during his Valencia days, netting clinically in first-half stoppage time to help Tottenham bounce back from consecutive home league losses to Newcastle United and Stoke City.
Vlad Chiriches, Nabil Bentaleb and Aaron Lennon came into the Tottenham team that triumphed at Hull, while Everton welcomed back Leighton Baines and Gareth Barry from respective hamstring and ankle complaints.
Ross Barkley pulled apart the Tottenham defence with a mazy 11th-minute run before Romelu Lukaku steered the loose ball at goalkeeper Hugo Lloris.
Another moment of brilliance gave Everton the lead when a Mirallas free-kick was cleared back to him and he cut inside Soldado, shifted the ball onto his right foot and curled an unstoppable strike into the top right corner via the crossbar.
Tottenham responded with conviction, not allowing discontent among a White Hart Lane faithful fearing another home setback to fester, and they were level in the 21st minute.
Aided by an intelligent Soldado run, Kane drove at a backpedalling Everton defence and Howard could only push his resulting shot towards Eriksen, who lifted a fine finish beyond defenders rushing back onto the line.
Kane was an energetic presence at the heart of most of Tottenham's good work and he tested Howard in the 30th minute before the wrong-footed keeper was glad to see a deflected Eriksen shot skip narrowly wide.
An ill-advised back-header from Muhamed Besic almost allowed Soldado to capitalise in the 37th minute, but the much-maligned forward made no mistake on the stroke of half-time.
Barry was dispossessed by Kane, allowing Lennon to surge forward and slip a perfectly weighted pass in for Soldado to finish first time.
Defender Federico Fazio might have netted his maiden Tottenham goal after the break, but failed to connect with Eriksen’s inviting cross following a well-worked corner routine.
Ryan Mason was the next man to be teed up by Eriksen and he blasted over with an hour played.
Barkley struck back in the battle of the playmakers by slotting Seamus Coleman in behind the Tottenham defence, but Lloris sprung from his line quickly to avert the 71st-minute danger.
Lukaku had a header blocked from Baines' 89th-minute free-kick, with the ball striking Fazio's arm in the area, but referee Michael Oliver was unmoved.
The result means Tottenham lie seventh in the Premier League table - three points better off than their opponents - and Mauricio Pochettino's team have won six of their past seven matches in all competitions ahead of Wednesday's short trip to face leaders Chelsea.
