Paulinho also made his Spurs debut in front of an almost capacity crowd at White Hart Lane, but Gareth Bale missed out due to injury as speculation continues to surround his future.
Brazilian midfielder Paulinho had the ball in the back of the net in the early stages, but his header was dubiously flagged for offside before Soldado opened the scoring from the penalty spot after Danny Rose was brought down inside the area.
Spurs dominated for the majority of the first half, but just seconds before the break, the game was level when David Lopez found himself unmarked at the near post to head home a corner from the right.
All in all it was a decent performance that suggested Tottenham are well-equipped for the season ahead, but their chances of finishing in the top four would be hugely enhanced, of course, if Andre Villas-Boas had his talisman, Bale, available.
The Welshman has been the subject of a summer-long pursuit by Real Madrid and was excluded from the Spurs matchday squad because of a foot injury.
But, with recovered long-term injury victims Younes Kaboul and Sandro both featuring, and the new signings all performing well, Spurs still have reason for optimism as they look to achieve the Champions League spot that slipped through their grasp last term.
After being paraded in front of a capacity crowd at White Hart Lane, Tottenham's three new signings impressed early on.
Paulinho thought he had given Tottenham the lead with a glancing header from Gylfi Sigurdsson's free-kick, but the effort was ruled out for offside even though replays showed the Brazilian was level.
Soldado then went close with a wicked header from Sigurdsson's cross.
Home goalkeeper Hugo Lloris had little do in the opening quarter as Spurs dominated the game with some fluid attacking play.
The pressure paid off just before the half-hour when Javi Lopez tripped Rose in the box and Soldado beat Kika Casilla from the penalty spot.
Apart from a long-range drive from Sergio Garcia, Espanyol were struggling to get in to the game but they stunned the home side by equalising on the stroke of half-time.
Lopez coasted to the near post to get between Soldado and Sigurdsson before thumping a header past Lloris. It was a sloppy goal to concede and the home crowd made their feelings known by booing.
Kaboul, who missed nearly all of last season with a knee injury, came on to a warm welcome at the break and he almost scored with a bullet header.
The game fizzled out thereafter, the only highlight being the return of Sandro for his first game of pre-season.
Rose had to come off near the end of the second half with concussion after an aerial challenge with Christian Stuani and both teams were content to settle for a draw.