In time added because of an injury to Liverpool defender Jamie Carragher, Robin van Persie's penalty put the home side in front just four minutes before Emmanuel Eboue shoved Lucas Leiva to the ground.
Dirk Kuyt equalized with the last kick of the match to leave Arsenal six points behind leader Manchester United with six games remaining. Chelsea is just two points further back in third place.
But while Arsenal could be set for a sixth straight season without a major trophy, Stoke has the chance of its first FA Cup title after the 148-year-old club beat Bolton 5-0 at Wembley to reach a final against Manchester City.
"We are used to being the underdogs," Stoke winger Matthew Etherington said. "We will be the underdogs in the final as well.
"Bring it on."
Etherington, Robert Huth and Kenwyne Jones all took advantage of poor defending to give Stoke, the Premier League's oldest club, a 3-0 lead inside 30 minutes.
Bolton goalkeeper Jussi Jaaskelainen was beaten for the fourth time in the 68th when Jon Walters blasted into the net from 25m.
Walters completed the rout nine minutes from the end.
After winning an FA Cup semifinal at the fourth attempt, Stoke will return to Wembley on May 14 to face a Manchester City side that defeated Manchester United 1-0 in the other semifinal on Saturday.
Both finalists are chasing their first major title since winning the League Cup in the 1970s. Stoke triumphed in 1972 and City emerged victorious four years later.
Meanwhile, Arsenal's streak without a trophy looks set to get another year longer.
"It looks like a defeat, it is true," Arsenal manager Arsene Wenger said. "It is a big test of character. I've had a few."
The start of the match was preceded by an immaculately observed minute's silence to honour former Arsenal director Danny Fiszman, who died this week, and the 22nd anniversary of the Hillsborough stadium disaster that killed 96 Liverpool fans.
Stan Kroenke, who assumed control of Arsenal this week partly through the purchase of Fiszman's shares, watched the match at Emirates Stadium but saw his new team show its old failings.
The Gunners created few clear chances against a Liverpool defence that remained robust despite the loss of Fabio Aurelio and Carragher, who was knocked unconscious in a clash of heads and had to be carried from the field.
But the otherwise impressive Jay Spearing tackled Arsenal captain Cesc Fabregas from behind to give Arsenal a penalty that Van Persie dispatched in the eighth minute of injury time.
Kuyt almost equalized straight from the kickoff with a shot from halfway that goalkeeper Wojciech Szczesny saved and Liverpool then won a free kick on the very edge of the area. It was blocked but Eboue shoved Lucas to give away the crucial penalty.
"I don't think there's any team anywhere can show the character and attitude and commitment our team's shown today," Liverpool manager Kenny Dalglish said.
Liverpool's intervention may have boosted fierce rival Manchester United's attempt to win a 19th English league championship and beat the record of 18 Liverpool set under Dalglish in 1990.
But Dalglish, whose team is now comfortable in sixth place, was unconcerned.
"We never handed anybody anything," Dalglish said. "We only look after ourselves. If anybody gets any advantage from our results, so be it.
"What matters is, we're still the best club in English football; in world football."
