King's 68th-minute header - his first goal in three years - and O'Hara's long-range shot in the final minute lifted Spurs three places in the standings and three points clear of relegation trouble, while the Hammers squandered a chance to climb six places to ninth.
For Redknapp, who played 149 times for West Ham from 1964, the victory followed the three in a row he had at Upton Park when he was manager of Portsmouth. All of Spurs' five victories of the season have come since he moved to Tottenham from Pompey and the club now lies 15th of the 20 Premier League teams.
"I want West Ham to win every week when I am not playing against them," Redknapp said. "I am more West Ham than anybody. It was a great result for us tonight. We needed it. It was a terrific performance from the players.
"I felt at halftime I wouldn't have settled for a point. I felt there was a win here for us tonight. We upped it a bit. When you have (Luka) Modric you want him on the ball and to get him into the game we did that in the second half. We looked solid. Ledley was strong at the back. I thought (West Ham striker) Carlton Cole was a threat, he was strong up front, but I couldn't see how else they would hurt us."
West Ham's latest loss has put pressure on Gianfranco Zola.
"I understand the fans' frustration," said the West Ham manager, who believed his team should have had a penalty for a handball by Benoit Assou-Ekotto. "We gave everything today to make them happy. It is not as easy situation for us, we know that. We will be working even harder than we have been. We won't panic."
Modric should have given Spurs the lead in the opening minute when a cross from Aaron Lennon found the Croat in front of goal but he shot weakly at goalkeeper Robert Green.
West Ham had the ball in the Spurs net in the 23rd minute when Tottenham midfielder Jermaine Jenas turned in a corner from Craig Bellamy into his own goal but referee Chris Foy whistled for a push by Hammers defender Lucas Neill.
A minute before halftime, Bentley forced Green into a diving block and Roman Pavlyuchenko then turned a cross from Lennon onto the post.
Spurs began to dominate in the second half, keeping the ball flowing toward the Hammers goal and deserved the lead in the 68th minute.
King rose to head home Lennon's cross from the right for the first goal West Ham had conceded in 340 minutes after three clean sheets. King had not scored since a 3-1 win over Portsmouth on Dec. 12, 2005.
Zola sent on Diego Tristan for his debut and had four forwards on the field to try and find an equalizer. The Hammers almost equalized two minutes from the end when Lucas Neill's close range shot was blocked by goalkeeper Heurelho Gomes.
From the clearance, however, Spurs made it 2-0 when O'Hara raced upfield and scored with a 25-meter (yard) shot.
In League Championship action, Crystal Palace beat Southampton 3-0 to climb to fifth and leave the Saints in 20th and close to the relegation zone.
