* Nine-man Tottenham Hotspur beaten 1-0 at Bournemouth
* Son Heung-min sent off for push just before halftime
* Substitute Juan Foyth shown red card just after the interval
* Nathan Ake headed late winner for the home side
* Spurs stayed third, four points clear of fifth-placed Arsenal
* Spurs host Everton on final day, Bournemouth face Crystal Palace (Adds quotes, details)
May 4 (Reuters)- Tottenham Hotspur had two men sent off and failed to make sure of a Premier League top-four finish after slipping to a 1-0 defeat by Bournemouth at the Vitality Stadium on Saturday.
With Chelsea, Arsenal and Manchester United — Tottenham’s rivals for third and fourth — not in action until Sunday, a win for Spurs on the south coast would have sealed a top-four finish and qualification for next season’s Champions League.
They dominated early on in the sunshine at the Vitality, but found Premier League debutant goalkeeper Mark Travers in inspired form for the hosts as the 19-year-old made a string of fine saves.
Tottenham’s task was made all the more difficult two minutes before the interval when forward Son Heung-min was sent off for pushing Jefferson Lerma and halftime substitute Juan Foyth lasted 125 seconds before seeing red for a lunging tackle.
Bournemouth struggled to make their numerical advantage count until Nathan Ake climbed highest to meet a corner and head a dramatic winner in the 90th minute.
Spurs, who trail Ajax Amsterdam 1-0 going into their Champions League semi-final second leg on Wednesday, stayed third, two points clear of Chelsea and four ahead of Arsenal with the top-four race set to go to the final day of the season.
“The first 40 minutes we played well and created chances but didn’t score,” Spurs manager Mauricio Pochettino said. “Then we know football can be cruel, they scored in the last minute.
“We need to move on. I will respect the decision of the referee (on the red cards).”
Travers, the first teenage goalkeeper to start a Premier League game since Joe Hart in 2006, produced a string of fine saves to deny Spurs an early goal.
A moment of madness from Son earned him a straight red card for shoving Lerma to the floor right in front of referee Craig Pawson.
Pawson was called into action again as he brandished the red card at Foyth for a dangerous lunge on Jack Simpson.
Spurs, though, looked comfortable in defence before poor marking at a corner allowed Ake to power home a header and send Tottenham to their 13th league defeat of the season.
“It’s important to do well against the top teams,” Ake said. “I think we want to do this more and it’s good we’ve done that today.” (Reporting by Peter Hall, editing by Ed Osmond)