Adebayor, recently recovered from a bout of Malaria, controlled and fired in Lewis Holtby's cross in the first half before Soldado headed in somewhat unnaturally in the second.
On 66 minutes, Andros Townsend cut inside and fired a wicked shot that Schalke keeper Ralph Farhmann beat on to Soldado's head, with the ball looping off him up into the air and down into the net.
The German side pulled a goal back through former Tottenham outcast Kevin Prince-Boateng, who fired past Hugo Lloris from inside the box with 10 minutes to go.
But a strong crowd at White Hart Lane would have been buoyed by a good performance from Mauricio Pochettino’s side.
The new head coach handed recent signing Eric Dier a pre-season debut at centre-back alongside Younes Kaboul, while Kyle Naughton and Danny Rose also featured in defence.
Other new arrivals Ben Davies and Michel Vorm were paraded in-front of the crowd along with Pochettino before the game but watched from the sidelines as Spurs controlled the game from the get-go.
Nabil Bentaleb, back after his spell at the World Cup with Algeria, sent an early effort from the edge of the box just wide before Adebayor struck just before the half-hour mark.
Lewis Holtby impressed in an attacking-midfield-four that also included Christian Eriksen, Erik Lamela and Aaron Lennon.
But Soldado, Davies, Townsend and Harry Kane came off the bench for the second half and Tottenham switched shapes with two strikers, yielding Soldado a goal after he missed with an earlier close-range chance.