Owen's goal, on 17 minutes, came after Riise lobbed the ball over a flat-footed Joos Valgaeren.
The Blades were still on top, and Matthew Lowton, Evans and Riise all went close late on.
The superb Bobby Zamora met Bjorn Helge Riise's cross with an assured finish to open the scoring.
And the Czech keeper demonstrated his value to Chelsea three minutes later with a brilliant block from Riise.
Fulham had taken the lead when Brede Hangeland headed home Bjorn Helge Riise's corner from six yards out.
But Riise headed in Salomon Kalou's cross five minutes into injury time to give Chelsea a priceless away goal.
Arsenal had their own lucky escape when John Arne Riise eluded the Arsenal defence to collect Dietmar Hamann's pass.
With Luis Garcia calling for the ball, Riise opted to shoot, an effort deflected away by Jens Lehmann's feet.
John Arne Riise had a long-range free-kick deflected just wide, but Liverpool were in danger of losing their early momentum.
Jamie Carragher and Ryan Babel had reasonable chances, while Torres and John Arne Riise were thwarted by some well-timed tackles.
Hodgson's side made a bright start with Bjorn Helge Riise continually finding room down Roma's right and causing them problems.
Yet Luton fought on and were rewarded when John Arne Riise bundled into his own goal from Drew Talbot's cross.
The Reds conceded an injury-time own goal by John Arne Riise in Tuesday's semi-final, first leg 1-1 draw at home.
Gerrard refused to put any blame on Riise for his mistake that handed a vital away goal to the Blues.
But Fulham held out and could even have grabbed a fourth when an unmarked Dempsey headed Riise's cross straight at Colomba.
Tyrone Mears proved just as diligent as he slid in to take the ball away from Riise as the Norwegian burst clear.
Zamora doubled the lead by heading in another Riise centre but Alexander Frei pulled one back from the spot after Chris Smalling handled.
Brayford did superbly to nod Collins' goal-bound header off the line and Doyle headed over from six yards following Bjorn Helge Riise's 18th-minute corner.
Luton survived another scare moments later with Brill making a good reaction stop after Riise's drive was deflected across the path of his dive.
Fulham substitute Eric Nevland later saw his shot turned around the post while Pizarro's cross was sent just wide by Riise at Schwarzer's far post.
The pressure told with Roma earning a penalty and a fine opportunity to equalise after Riise broke dangerously in the box and was tripped by Kelly.
And Fulham eventually buckled when John Arne Riise's shot took deflections off Gera and his brother Bjorn on the way past wrong-footed Cottagers keeper Mark Schwarzer.
Kalou's cross sparked uncertainty in the six-yard area and Riise, in two minds, sent a spectacular flying header into the top corner at the Kop end.
This sparked Roma into life and Bjorn Helge Riise's brother, John Arne, forced a fine save from Schwarzer with a half-volley from the edge of the area.
And eventually they got their reward when Hangeland out jumped both the Roma defence and keeper Doni to head Riise's corner into the back of the net.
But Nevland was sent off for a 49th minute tackle on Daniele de Rossi before John Arne Riise equalised with a shot that deflected off two players.
Riise's late blunder at Anfield in the 95th minute changed the complexion of the tie after Dirk Kuyt had put the Reds ahead in the first half.
Riise should have scored the winner soon after but flashed a left-foot shot narrowly wide of Brill's post and Edwards went close for Luton with a dipping volley.
Crouch headed tamely at Cech when he should have done better, and he was slow to react when a Riise thunderbolt rattled back off the bar on the hour.
The game was more open up after the interval and Samba might have done better when John Arne Riise failed to clear, but the Blackburn defender delayed his shot.
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