Despite initially going ahead in the early stages through Lewis Holtby, Spurs struggled with Sounders' agile frontline and had to rely on two second-half penalties to avoid defeat.
The two sides played out a vibrant, entertaining encounter at CenturyLink Field in Seattle, with both sides playing attractive football in front of a packed crowd of over 55,000 fans.
Xander Bailey, an18-year-old beneficiary of the Make-A-Wish Foundation took the kick-off with his hero Clint Dempsey and the Sounders looked very lively in the early stages.
Nevertheless, Spurs took the lead with only 10 minutes on the clock as Holtby nodded in Harry Kane's left-wing cross from 10 yards.
Goalkeepers Brad Friedel and Stefan Frei were both forced into a couple of saves over the following 10 minutes, but it was the Spurs man who was the next to pick the ball out of his net.
Michael Dawson fouled Chad Marshall at a corner and former Mexico international wing-back Gonzalo Pineda coolly netted the resulting penalty with a clever chip.
Sounders took the lead for the first time just after the break as Osvaldo Alonso found the top corner from 30 yards in emphatic fashion, but Spurs wasted no time in restoring parity.
With 54 minutes on the clock, Roberto Soldado was sent tumbling in the area by Marshall after a neat touch had taken him clear, and the much-maligned Spaniard converted the spot-kick.
Substitute Tristan Bowen's tap-in looked to have claimed a late victory for Sounders, but Falque confidently dispatched the game's third spot-kick following DeAndre Yedlin's handball and the match ended level.
Spurs will continue their tour of North America with a clash against Toronto on Thursday.