Lewis Holtby’s early opener was cancelled out by Gonzalo Pineda and Seattle then took the lead through Osvaldo Alonso, before Roberto Soldado equalised.
The drama was not over, though, as Tristan Bowen made it 3-2 to the home side and Spurs hit back once again thanks to Iago Falque.
There was a special moment at the start of the match as Seattle, currently top of the Western Conference in Major League Soccer, kicked off with 18-year-old Xander Bailey.
The midfielder, who signed a professional deal the previous day as part of the Make-a-Wish Foundation, ran through and drew a save from American goalkeeper Brad Friedel before leaving the field to huge cheers.
It took just ten minutes for Spurs to go in front as Holtby darted between two defenders to latch on to a beautifully weighted cross from Harry Kane and head in confidently.
For the rest of the first half there were signs of Seattle’s superior sharpness against a Spurs side at the start of their pre-season campaign, as former Tottenham player Clint Dempsey headed wide, Lamar Neagle had a shot saved and ex-Newcastle United man Obafemi Martins fired of target.
The equaliser came from the penalty spot after 32 minutes when Michael Dawson fouled Chad Marshall and Pineda chipped the coolest of spot-kicks straight down the middle as Friedel dived to his side.
Danny Rose cleared Dempsey’s shot off the line before half-time, when Pochettino made a host of changes.
The substitutions failed to have an immediate impact, though, as Alonso put Seattle ahead in the 48th minute with a tremendous strike from distance into the top corner.
Spurs drew level five minutes later as Soldado was bundled over in the box by Marshall and he stepped up to tuck away the penalty.
Tottenham threatened sporadically to take the lead but it was Seattle who struck next as Bowen turned in Sean Okoli’s low cross from close range in the 78th minute.
However, Seattle were again unable to protect their advantage as DeAndre Yedlin conceded the third penalty of the match for handball a moment later and Falque slotted into the bottom corner to secure a draw.
Pochettino was content with his side's performance despite conceding three goals.
He told the club's official website: "I’m happy as it was the first game of the tour, the conditions were difficult with warm temperatures and all the players did their best.
"This is the time to improve and learn and I'm very pleased with all the players."