Manchester United added to Chelsea woes by beating their rivals in Avram Grant's first game in charge of the Blues after Jose Mourinho's exit.
Tevez nods in for his first goal for Man Utd
Chelsea put in a resolute showing but had Mikel Jon Obi harshly sent off for a rash tackle on Patrice Evra.
United then went ahead after first-half injury-time had elapsed with a near-post Carlos Tevez header.
Chelsea stubbornly kept the deficit to one goal until Louis Saha's spot-kick after a foul on him by Tal Ben Haim.
The Chelsea players had been firmly under the microscope at the start of the game after Mourinho's exit and came away with their pride intact after a battling display.
They traded high-fives and hugs in a show of unity as they gathered together just before kick-off.
If there was any fragility about the Blues' resolve, a professional United quickly tried to expose it as they took a stranglehold of the game.
United striker Wayne Rooney cut inside Ben Haim on the edge of the box and curled a shot on the visitors goal which keeper Petr Cech finger-tipped wide at full-stretch.
Chelsea heeded the warning and duly got into their stride, producing some promising periods of play - only to squander their good work with poor decisions and a lack of a cutting edge in the final third.
The home side were denied a penalty when a sliding Joe Cole appeared to make contact with Evra ahead of getting a touch on the ball, before Giggs then wasted a gilt-edged chance.
Michael Essien gave the ball away to Rooney and he crossed for Giggs, who side-footed a volley high from a tight angle at the far post.
Referee Mike Dean sends off Mikel to reduce Chelsea to 10 men
Chelsea suffered a setback when Mikel was sent off when he led with his studs as he chased down the ball and their resistance finally buckled on the stroke of half-time.
Giggs curled an outswinging cross to the near post with the outside of his left foot and Tevez got his head to the ball before Cech to head in his first goal for the club.
Chelsea will be unhappy referee Mike Dean did not blow for half-time before the goal as the allotted two minutes of added time had already elapsed.
United pressed for a second after the break and Giggs blazed a volley high but the home side struggled to create chances as a determined Chelsea held them at arm's length.
Joe Cole was fortunate to stay on the pitch for a lunge at Cristiano Ronaldo as Chelsea hoped to snatch an equaliser.
But the visitors' hopes were ended when Saha stroked in a penalty to move United up to second and leave the visitors five points adrift of top place in the Premier League.
Man Utd: Van der Sar, Brown, Ferdinand, Vidic, Evra, Ronaldo, Scholes, Carrick, Giggs, Tevez (Saha 79), Rooney.
Subs Not Used: Kuszczak, Nani, Pique, O'Shea.
Booked: Rooney, Brown.
Goals: Tevez 45, Saha 90 pen.
Chelsea: Cech, Ferreira, Ben-Haim, Terry, Ashley Cole, Makelele, Essien, Obi, Joe Cole (Pizarro 76), Shevchenko (Kalou 59), Malouda (Wright-Phillips 69).
Subs Not Used: Cudicini, Alex.
Sent Off: Obi (32).
Booked: Joe Cole, Terry.
Ref: Mike Dean (Wirral).