Jermain Defoe saw his stoppage-time penalty kick saved by Green to leave Spurs still looking for their first away win of the season.
On their last visit to Upton Park back in early March, Spurs had left the heartbroken Hammers rock-bottom of the Premiership thanks to a dramatic injury-time winner, but this around Green's third successive penalty save of the season earned the East Enders the point that they so easily deserved.
Indeed, nine months on, West Ham came into this contest four places above the north Londoners and, following his side's thumping five-goal victory at Derby County a fortnight ago, there was more good news for Alan Curbishley in the shape of fit-again midfielders Mark Noble and Hayden Mullins, while Dean Ashton and Scott Parker returned to the bench.
Following their 4-0 win over Wigan Athletic, Spurs had made just one change as Gareth Bale returned in place of Young-Pyo Lee, and Juande Ramos must have thought that they were on their way, when Aaron Lennon put the ball into the net after just four minutes but the effort was ruled out by an offside flag.
On 20 minutes, though, Carlton Cole had no such problems when he tapped home his third goal of the season after Luis Boa Morte took advantage of an error by Younes Kaboul before playing in the overlapping Nolberto Solano, who squared the ball to the unmarked Hammers' striker on the edge of the six-yard box.
Paul Robinson had been dropped by England in midweek but, clearly determined to bounce back, he confidently denied Mullins before blocking Boa Morte's powerful, close-range, angled strike with his knees.
Apart from seeing Dimitar Berbatov carelessly slice high and wide, Spurs offered little, but as the interval approached Robbie Keane had his vociferous claims for a penalty waved away, when he was upended by the advancing Green after he broke clear and lobbed the ball wide of both the Hammers' 'keeper and the left-hand post.
Ten minutes into the second half, Ramos brought on Darren Bent in place of Kaboul and midway through the half Spurs equalised when Jermaine Jenas fired a deep free-kick into the heavily populated Hammers' area, where Michael Dawson climbed in front of the Green to beat the red-faced keeper's attempted punch and level with a looping header.
The Hammers' keeper soon atoned for that misjudgement with a brilliant stop to deny Steed Malbranque's scorcher, while at the other end Cole fired wide, Jenas cleared off the line from George McCartney and both Ashton and Parker saw their shots tipped aside by Robinson.
Defoe had replaced Keane for the final ten minutes and after becoming the seventh player to be booked in this feisty derby, he then hit the turf under the challenge of Lucas Neill in stoppage time.
Amid a crescendo of boos, he picked himself up and placed the ball on the spot, but just when it looked like he was about to give Spurs that elusive first away win of the season, Green dived low to his left to preserve a point for the Hammers with that third successive penalty save.