Costa Nhamoinesu's 11th-minute strike proved to be the only goal of the game as Sparta booked their place in the last 32 as Group K winners, leaving Southampton needing a win or a 0-0 draw against Hapoel Be'er Sheva in their final group game next month.
Southampton went into the match as one of only six teams yet to score an away goal in the Europa League this season, but they had a chance to break the duck less than three minutes in when Shane Long and Jordy Clasie combined to find Jay Rodriguez, but his touch was poor and allowed the defence to get back and make a challenge.
Sparta responded with a chance of their own at the other end moments later when David Lafata almost capitalised on a risky header from Pierre-Emile Hojbjerg, but the striker just couldn't connect with the ball.
The opening goal did arrive for the hosts in the 11th minute, though, as Borek Dockal lifted a free kick into the box for Costa, who escaped his marker before volleying past Fraser Forster at the near post.
Sparta were content to sit back after taking the lead and Southampton began to dominate possession without being able to find a way through in the opening 45 minutes.
Their best work came down the left flank, with Sam McQueen breaking into the box on a couple of occasions but firing his first shot straight at the keeper before dragging another effort wide midway through the half.
Long also saw a looping header tipped past the post by the keeper, but for the most part Southampton were frustrated and limited to tame long-range strikes from James Ward-Prowse and Clasie.
The second half quickly fell into a similar rhythm, although it was Sparta who began to look the most like scoring as the half progressed, with Forster the busier of the two goalkeepers.
The Southampton shot-stopper was fortunate that the ball fell to a teammate when he could only parry a Vyacheslav Karavaev effort into a dangerous area, but he reacted well shortly afterwards to keep out a free kick that threatened to creep in after Lafata failed to get a touch.
Sparta's attacks were rarer than Southampton's, but they did carry a greater threat and Lukas Marecek was inches away from doubling his side's lead with an effort from the edge of the box that flew narrowly wide of the target.
Forster was called into action once again three minutes later when the Saints failed to clear their lines and the ball dropped to Dockal, but the keeper was equal to the low strike.
Southampton finally created their first chance of the second half with just 11 minutes remaining when Virgil van Dijk climbed highest in the area to get on the end of a corner, but he couldn't keep his header down when he should have done better.
That proved to be the last sight of goal for the visitors as they made it six away games in a row without victory in all competitions and four goalless games in succession on the road in Europe.
Hapoel Be'er Sheva's comeback victory over Inter Milan means that the Israeli outfit are now level on points with Southampton ahead of the St Mary's showdown next month, with a score draw being enough to send the the Premier League club out due to the head-to-head rule.
Sparta, meanwhile will definitely progress into the knockout stages as group winners courtesy of a sixth consecutive home victory, while they have also kept five successive clean sheets across all competitions for the first time since September 2008.
The Czech outfit, who have beaten English opposition for the first time in their last 16 attempts dating back to 1983, will face Inter Milan at San Siro in their final group game, with the fate of both teams already decided.