A delighted Roy Hodgson has now taken 13 points from his eight matches in charge to propel the West Midlanders to the brink of safety.
"It was a splendid result to come back from 2-1 down," Hodgson said.
"It's given us what looks to be an important point given the way other results have gone.
"It has taken us to a psychological point at least, which is 40 [points]. A lot of people would say that is enough [to save us from relegation] but I think we might need a point or two more."
Peter Odemwingie's 13th goal of the season gave the Baggies the lead before Roman Pavlyuchenko equalised in the 27th minute with a well taken strike that flew in off Scott Carson's far post.
Jermain Defoe scored his 100th Spurs goal with 25 minutes left to put the hosts 2-1 up.
Simon Cox has struggled to make an impact since he signed from Swindon two years ago but Redknapp thinks the 23-year-old should savour his first Barclays Premier League goal.
"It was a world-class strike," Harry Redknapp said.
"Before that, there was no panic. We even looked like we were going to score again.

