Third-tier struggler Oldham stunned Liverpool with a 3-2 win while Spurs lost 2-1 at Leeds, which is mid-table in the second-tier League Championship. Chelsea was spared a similar fate by Spain striker Fernando Torres, who earned the holders a replay with a late equalizer in a 2-2 draw at third-tier Brentford.
The FA Cup has been made famous down the years for so-called "giant killing acts" and this season has proved no different, with non-league team Luton beating Norwich away 1-0 on Saturday and both Aston Villa and Queens Park Rangers also falling to lowly sides.
Fourth-tier Bradford set the tone this season by reaching the League Cup final after knocking out both Arsenal and Aston Villa, giving its peers hope of beating the country's big names.
"You have to take it on the chin, but there has been plenty of warnings throughout the weekend," Liverpool manager Brendan Rodgers said. "If your application is not right, you can get found out."
Both Liverpool and Tottenham fielded weakened lineups but they still contained a raft of internationals and millionaire players, who didn't appear to be up for the fight until it was too late.
"I am left speechless by the result," said Oldham striker Matt Smith, who scored twice for a team that is 55 places lower than Liverpool in English football's rankings. "We went out there wanting to battle together."
Oldham made its name in the early 1990s when the club reached two FA Cup semifinals (1990 and '94) and a League Cup final ('90), where it lost to Nottingham Forest.
The team managed by former Manchester City striker Paul Dickov revived those memories by going ahead through Smith in the third minute, then taking a 3-1 lead after Luis Suarez — who captained Liverpool for the game with Steven Gerrard on the bench — equalized.
Joe Allen's deflected goal in the 80th set up a tense closing stage but Oldham saw off a flurry of attacks to set up a fifth-round match with another Merseyside team — Everton.
"There are a lot of emotions at the minute," said Dickov, whose team has lost seven of its last eight matches. "I am very proud and I am very pleased for the fans as it has been a long time without success for them."
Tottenham, which is fourth in the Premier League, is the highest-ranked team out, paying the price for playing no recognized striker at Elland Road.
Luke Varney raced through to put the hosts ahead in the 15th minute and Ross McCormack also broke the offside trap to cut inside and curl a fine shot into the corner in the 50th.
With Jermain Defoe out injured and Emmanuel Adebayor at the African Cup of Nations, Clint Dempsey played out of position as a striker and headed in Gareth Bale's cross in the 58th to give Spurs hope.
"It was a fabulous performance," Leeds manager Neil Warnock said. "It was a fabulous cup tie, they gave everything. There were a lot of heroes today and we enjoyed it."
Chelsea, which has won four of the past six FA Cups, scraped through to a replay despite putting in a rudderless display against a west London rival that is third in League One.
The European champions were outplayed at times on a sandy pitch and were forced to come from behind twice in the second half, with Brazil midfielder Oscar grabbing the first equalizer in the 55th and Torres ending an eight-match barren run to make it 2-2.
"In the first half, we didn't do what we had to do," said Chelsea manager Rafa Benitez, who was the target of abuse from visiting fans throughout the match. "We made too many mistakes, but I was really pleased with the reaction of the team after that. We showed quality and character."
The replay will be played on the same weekend as the fifth-round matches on Feb. 16-17 since the next three midweeks are filled with fixtures in the Premier League, international football and the Europa League.
"There is a football god up there and he is on our side," said Brentford manager Uwe Rosler, another former Man City striker.
"Overall, my players did fantastically. They earned the right to play at Stamford Bridge. It will be a great day for our supporters again, for our players and, financially, it will help enormously."