Second-half goals from skipper Ledley King, his first for three years, and youngster Jamie O'Hara gave visiting Tottenham a deserved victory as they climbed to 15th by virtue of a superior goal difference over their London rivals.
West Ham, who next face a daunting trip to Chelsea on Sunday, have now won just once in their last 10 league games as the pressure begins to mount on manager Gianfranco Zola.
Their slump in form is in sharp contrast to Tottenham's surge under Redknapp, who took charge when Spaniard Juande Ramos was sacked after collecting two points from the first eight games of the season.
In eight matches under former West Ham boss Redknapp, Spurs have taken 16 points and have reached the semi-final of the League Cup.
West Ham enjoyed plenty of possession but Spurs should have taken the lead before halftime when Roman Pavlyuchenko slid in to turn an Aaron Lennon cross against the post.
Lennon was dangerous throughout and it was his centre after 68 minutes that allowed King to head powerfully past keeper Robert Green.
West Ham almost grabbed a late equaliser when Lucas Neill's shot was well saved by Heurelho Gomes and David Di Michele could only turn the rebound straight at the Brazilian keeper.
After that let-off Tottenham launched a quick counter-attack in the 89th minute, ending with substitute O'Hara smashing a left-foot shot past Green.
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