PENALTY TO SOUTHAMPTONpublished at 55 mins
James Ward-Prowse takes the ball past Kian Hansen, who brings him down with a swinging kick on the edge of the box. Clumsy and arguably needless.
Rodriguez's first goal since March 2014
Crisp low strike from ex-Saint Sparv
Winner joins Spurs & Liverpool in group stages
Second leg is next Thursday
Emlyn Begley
James Ward-Prowse takes the ball past Kian Hansen, who brings him down with a swinging kick on the edge of the box. Clumsy and arguably needless.
And we have an equaliser. Dortmund may at one point have trailed 3-0 to Odd in Norway but the German side have shown great tenacity to pull themselves level - Pierre-Emerick Aubameyang with the leveller, his second of the night.
Dortmund have hit the woodwork three times too.
Southampton looking better now and Graziano Pelle loses his marker to head Jay Rodriguez's cross but it's straight at keeper Johan Dahlin.
The corner comes in and Southampton defender Steven Caulker heads home. It's ruled out for a foul on Petter Andersson although the referee didn't make it very clear for a few seconds if he was awarding the goal or not.
Sadio Mane picks out Graziano Pelle on the edge of the box, the Saints striker swivels and shoots and it's deflected wide by Tim Sparv. Corner.
Southampton start the half in an attacking mode but Midtjylland go up the other end and Saints just about clear a Kian Hansen throw-in with Erik Sviatchenko lining up a bicycle kick.
I've seen Hansen compared to Rory Delap in the build-up to this match - not sure his throw-ins are quite as good.
I said there are 190 fans supporting the Danes - I've seen plenty of Brentford fans in the away end. Apparently the Bees sold 55 tickets for this game.
Brentford owner Matthew Benham is the majority shareholder for Midtjylland.
Southampton get the second half under way. Doesn't look like either side have made any changes.
Saints have tweeted that the attendance is 28,890, with 190 of those supporting the Danes.
The goal was only Midtjylland's second shot on target.
Adam Williams
BBC Sport at St Mary's
Shockwaves around St Mary's right on the stroke of half-time as FC Midtjylland take the lead through Southampton academy graduate Tim Sparv.
For all Southampton's energy throughout that first 45 minutes there was a definite absence of an end product and now the Danes have punished them.
You can't say they haven't deserved it for their efforts and now they have a precious away goal to show for it.
Time to take the Europa League seriously?
Is that the first instance of a player refusing to celebrate against an old club he never actually played a game for?
That's the last action of the half. A hammer blow for Southampton.
Tim Sparv scores a cracker against his old club from 25 yards but doesn't celebrate because he spent three years with the Saints academy as a kid, despite never making a first-team appearance.
Saints captain Jose Fonte headed a cross straight to the Finn, who made him pay. The defender won't be happy with his contribution there.
James Ward-Prowse plays a short corner to Sadio Mane, who plays the ball back to the midfielder. His cross is headed clear to Oriol Romeu, who has a good effort from 20 yards but it's saved by Pione Sisto.
It's been a while since Midtjylland have done anything going forward.
Sadio Mane plays a one-two with a team-mate and tries to curl the ball in from 20 yards out but he forgets the curl and it's down the middle at keeper Johan Dahlin.
Southampton won't want half-time to come - they're doing all the attacking now.