Chelsea had seemed on course for a 1-0 win after a 36th-minute Wayne Bridge goal but were stunned 13 minutes from time when Jermaine Easter trickled a shot past Hilario.
Chelsea, who have drawn their last three league games to slip six points behind Manchester United, will still expect to progress.
But Wycombe, who knocked out Premier League Fulham and Charlton Athletic on their own grounds earlier in the competition, will visit Stamford Bridge for the second leg unfazed by their millionaire opponents.
The return game takes place on January 23 with the winners playing Arsenal or Tottenham Hotspur in the February 25 final at Cardiff's Millennium Stadium.
"I thought we were absolutely brilliant, to come back against a world class side like that," Wycombe coach Paul Lambert told Sky Sports.
"It is going to be 10 times harder than tonight (in the second leg) but we've kept the tie alive."
Chelsea coach Jose Mourinho did not seem unduly disappointed by the shock result. "I prefer to win than draw but a draw in a two leg semi-final is a draw and now we have to decide things at home," he said.
"In a semi-final there are no teams from first division second or third, for me every team is from the same competition so I think it was a good result away from home," added the Portuguese coach, who said he picked his strongest available team from an injury-hit squad.
BRAVE BRIDGE
Wycombe, who reached the FA Cup semi-finals in 2001, started full of running and verve but Chelsea absorbed the early pressure and, after Bridge had seen an effort cleared off the line, duly went ahead.
Salomon Kalou exposed the home defence with a long ball into the path of Bridge and as goalkeeper Ricardo Batista charged out, Bridge bravely kept his eye on the ball to hook it beyond the keeper and into the net.
The former England fullback, operating in midfield on Wednesday, did not see the ball cross the line, however, as Batista crashed into him, splitting his nose and knocking him out, with the keeper also needing stitches.
Chelsea were without any of their regular centre backs through injury and suspension but stand-ins Paulo Ferreira and Michael Essien initially looked comfortable enough and the rest of the side was of the highest pedigree.
But the makeshift defence was exposed five minutes into the second half when Tommy Mooney's pass set up Matt Bloomfield inside the box and although he sliced wide of the target it gave the hosts new belief.
Chelsea's 17-year-old Israeli striker Ben Sahar had a chance to double their lead after a swift counter-attack in the 70th minute but the substitute shot tamely at the keeper.
Wycombe took full advantage seven minutes later when Easter ran on to a flick from Mooney, outmuscled Essien and got just enough on his shot to send the ball beyond Hilario and over the line.
The Welsh striker, formerly at Hartlepool, Cambridge, Boston and Stockport, has scored in every round of the competition this season and his latest effort sent the crowd wild and spurred his team into a furious, though fruitless, late effort to grab a winner.
