Rangers will start the second leg at Ibrox next Thursday on level terms and with an away goal after Filip Helander's first-half strike.
Nicolae Stanciu's classy early strike brought Steven Gerrard's side back down to earth, four days after Rangers ended a 10-year wait to be crowned champions of Scotland again.
Helander levelled in a first half where Slavia - conquerors of Leicester City in the previous round - had much the better of the play at Sinobo Stadium, yet an improved Rangers wasted chances to win it after the interval.
Defender Helander's goal means Rangers could be considered to hold an advantage ahead of the second leg at Ibrox in seven days' time, with Slavia unbeaten in 29 home games but left to rue not being able to build on such a great start.
Stanciu stunned Rangers when he bent a sumptuous right-footed finish into the far corner of the net from just outside the penalty area in the seventh minute.
Jindrich Trpisovsky's side would not let Rangers settle and Lukas Provod prodded tamely wide before he tested Allan McGregor with a free-kick from wide on the right.
The Glasgow giants warmed to the task and they were level nine minutes before the break, when Slavia failed to deal with Borna Barisic's free-kick and the alert Ianis Hagi squared to set up Helander for a tap-in.
Slavia suffered a blow when David Zima was booked for upending the industrious Alfredo Morelos, ruling him out of the second leg, before Joe Aribo sliced wide just after the hour mark.
The lively Aribo was causing Slavia problems and Ryan Kent met his cutback with a scuffed left-footed shot that was brilliant palmed away by Ondrej Kolar when it looked destined to find the far corner.
Rangers were firmly on top and Connor Goldson somehow failed to get a head on Barisic's brilliant whipped free-kick.
Yet the visitors were relieved when McGregor brilliantly kept out Lukas Masopust's downward header in the closing stages to ensure it ended honours even.
What does it mean?
Gerrard will surely be more than happy to be heading home on level terms after Slavia made such an ominous start.
Rangers are now unbeaten in their last 18 matches of what is turning out to be a magnificent season, while Slavia have gone 17 games without defeat.
Something will have to give at Ibrox, where Rangers will attempt to avoid crashing out at this stage for the second successive season.
All-action Aribo carries Gers fight
Midfielder Aribo was in the thick of the action as Rangers raised their game after the interval and could easily have claimed a first-leg advantage.
He showed great awareness to pick out Kent, who came so close to a winner, and won half of his 12 duels in an energetic display.
Zima out of the frame for second leg
Slavia will have to do without Zima in Glasgow next Thursday following his rash tackle on Morelos.
The defender had his hands full as Morelos led the line tirelessly, but he will be missed by the Czech champions in the return fixture.
Key Opta facts
- Rangers have gained their first ever positive result in European competition away to sides from the Czech Republic, having lost their previous three such matches without scoring.
- Rangers' leveller from Helander was the Scottish side's eighth goal by a defender in the Europa League this season, which at full-time was more than any other team had achieved.
- Slavia's Stanciu has been directly involved in nine goals (five goals, four assists) in his 11 Europa League home games - indeed 75 per cent of his goal involvements in the competition have come on home soil (9/12).
Leaders Slavia take on Mlada Boleslav in the Czech First League on Sunday, while the Gers are not in action until the second leg.