Andreu was denied from the spot by a brilliant save from Raith keeper Kevin Cuthbert 15 minutes from time.
United were reduced to ten men when former Rovers defender Lewis Toshney was sent off in 55 minutes after collecting a second yellow card.
Rudi Skacel struck the bar for Raith but neither side could find the net.
Dundee United manager Ray McKinnon is desperate to add more of a goal threat to his team and Dutch trialist striker Felitciano Zschusschen watched from the stands.
The Tangerines struggled to make clear cut chances but with 15 minutes to go Scott Fraser went down in the box as he tried to go between Jean Yves M'Voto and Kyle Benedictus.
Cuthbert produced an impressive save to deny Norwich City's on-loan striker Andreu to ensure the points were shared.
Raith Rovers manager Gary Locke: "It was a great save from Kevin but he shouldn't have had to make it. It was a poor decision.
"I'm not one that likes to go about these things as the referees have got a hard job and it's not something I want to talk about too much but it was a soft, soft decision.
"It was great that he saved it though as we wouldn't have deserved to get beat in that game."
Dundee United manager Ray McKinnon: "I'm so proud of the players today as I thought we were the better team for the entire 90 minutes and even when we were down to ten men we were excellent.
"We created a few chances but there will be twists and turns in this league all season and we have lots of positives to take forward.
"To get a point against a tough team like Raith with just ten men was absolutely outstanding and if you had said to us three months ago we would be up at the top of the league we would have taken that."
Match ends, Raith Rovers 0, Dundee United 0.
Second Half ends, Raith Rovers 0, Dundee United 0.
Attempt missed. Ross Callachan (Raith Rovers) left footed shot from the centre of the box is just a bit too high.
Substitution, Raith Rovers. Joel Coustrain replaces Bobby Barr.
Corner,  Raith Rovers. Conceded by Sean Dillon.
Corner,  Raith Rovers. Conceded by Scott Fraser.
Ross Matthews (Raith Rovers) wins a free kick on the left wing.
Foul by Sean Dillon (Dundee United).
Attempt saved. Simon Murray (Dundee United) right footed shot from the centre of the box is saved in the bottom right corner.
Tony Andreu (Dundee United) wins a free kick in the defensive half.
Foul by Jordan Thompson (Raith Rovers).
Attempt saved. Kyle Benedictus (Raith Rovers) header from the centre of the box is saved in the top centre of the goal.
Corner,  Raith Rovers. Conceded by Mark Durnan.
Blair Spittal (Dundee United) wins a free kick on the right wing.
Foul by Jordan Thompson (Raith Rovers).
Substitution, Raith Rovers. Lewis Vaughan replaces Declan McManus.
Hand ball by Declan McManus (Raith Rovers).
Declan McManus (Raith Rovers) is shown the yellow card for a bad foul.
Blair Spittal (Dundee United) wins a free kick in the defensive half.
Foul by Declan McManus (Raith Rovers).
Attempt missed. Chris Johnston (Raith Rovers) left footed shot from outside the box is close, but misses the top right corner.
Foul by William Edjenguele (Dundee United).
Mark Stewart (Raith Rovers) wins a free kick in the attacking half.
Attempt saved. Declan McManus (Raith Rovers) header from the centre of the box is saved in the centre of the goal.
Hand ball by Declan McManus (Raith Rovers).
Corner,  Dundee United. Conceded by Iain Davidson.
Attempt missed. Mark Durnan (Dundee United) header from the centre of the box is too high.
Corner,  Dundee United. Conceded by Kevin Cuthbert.
Kyle Benedictus (Raith Rovers) is shown the yellow card for a bad foul.
Penalty saved! Tony Andreu (Dundee United) fails to capitalise on this great opportunity,  right footed shot saved  in the bottom left corner.
Penalty Dundee United. Simon Murray draws a foul in the penalty area.
Penalty conceded by Kyle Benedictus (Raith Rovers) after a foul in the penalty area.
Attempt blocked. Scott Fraser (Dundee United) right footed shot from outside the box is blocked.
Hand ball by Ross Callachan (Raith Rovers).
Substitution, Raith Rovers. Mark Stewart replaces Rudi Skacel.
Attempt missed. Tony Andreu (Dundee United) right footed shot from outside the box is close, but misses to the right.
Attempt blocked. Rudi Skacel (Raith Rovers) left footed shot from outside the box is blocked.
Attempt missed. Blair Spittal (Dundee United) left footed shot from outside the box is close, but misses to the right.
Attempt missed. Declan McManus (Raith Rovers) header from the centre of the box is close, but misses to the right.
Attempt blocked. Tony Andreu (Dundee United) right footed shot from outside the box is blocked.
Tony Andreu missed a second-half penalty as Dundee United dropped two points in the Championship title race with a draw at Stark's Park.