The Chairboys looked as though they would have a healthy lead to take back to Adams Park as goals from Paul Hayes, Aaron Holloway and Steven Craig put them 3-0 ahead.
But Plymouth revived their hopes of reaching Wembley thanks to late strikes from substitutes Zak Ansah and Jason Banton.
The return leg takes place on Thursday evening.
Plymouth ended the League Two campaign 13 points adrift of fourth-placed Wycombe in seventh but they had won 2-0 in Buckinghamshire in February and were encouraged by the biggest crowd at Home Park – 14,175 – since their relegation from the Championship five years ago.
And Plymouth were quick to pile the crosses in on young Welsh goalkeeper Alex Lynch who had been called up for his first senior start after a knee injury prevented Matt Ingram from making his 112th consecutive appearance in the Wycombe goal.
Pilgrims skipper Curtis Nelson headed wide in the second minute before Lewis Alessandra failed to keep Kelvin Mellor’s cross down as John Sheridan’s side made in-roads down both flanks.
But the mood inside Home Park changed in the 10th minute when Alfie Mawson met Joe Jacobson’s corner, Luke McCormick blocked the point-blank effort but Hayes bundled home the rebound from close range.
Wycombe doubled their lead after 22 minutes in controversial fashion as the Pilgrims almost stopped to a man when Craig appeared to control a free-kick with his arm, but referee Peter Bankes allowed the game to continue and Holloway delivered a wonderful low strike beyond McCormick.
Plymouth struck the woodwork after 29 minutes when Carl McHugh rose highest at a corner but the referee had spotted that he had used his arm to send the ball onto the bar and the midfielder was promptly booked.
There was no lack of energy in Plymouth’s attacks but they lacked the invention to open up a sturdy Wycombe defence which was doing a manful job of protecting Lynch.
Bobby Reid did find a yard of space five minutes before the break to send the ball goalwards but not for the first time a Wycombe defender was in the right place to block.
Injury forced off Hayes at half-time but it failed to knock Wycombe out of their stride and Craig profited after 52 minutes when Sam Saunders slipped him through on the right side of the penalty area.
Craig’s goal served to deflate the Pilgrims who were suddenly second-best all over the field and were unable to make the sort of headway they had done in the first half.
Substitute Matt Bloomfield might have added a fourth for Wycombe and Plymouth appeared a spent force, but Ansah gave them hope with a wonderful 25-yard strike before Banton curled home a second past the flat-footed Lynch in the final moments.