Leverkusen, which has already wrapped up the Bundesliga title and will contest the DFB-Pokal final on 26 May (AEST), stretched its unbeaten run through all competitions this season to 49 matches, surpassing Benfica's long-standing European top-tier record set between 1963 and 1965.

Once again, it did it the hard way after two Leandro Paredes penalties wiped out a first-leg advantage, with a Gianluca Mancini own goal and a stoppage-time strike from Josip Stanisic completing a dramatic comeback.

After its 4-2 aggregate victory, Roma will face Atalanta in the 23 May (AEST) final in Dublin, after La Dea overcame Marseille 4-1 on aggregate in the other semi-final.

"We'll play two finals in a week as a result," Alonso said. "We showed great character today after their second goal. 

"I looked my players in the eye afterwards and saw that they wanted more.

"We still have the chance to win three titles, and my boys deserve all three titles."

Despite going 3-2 up on aggregate when Mancini put through his own net, Leverkusen refused to sit back as it looked to preserve its unbeaten record, which it did through Stanisic's 97th-minute strike.

Asked whether that goal was one of the biggest moments of his career, the Bayern Munich loanee said: "Definitely one of them. 

"We knew what was at stake, we really wanted to get to the final and I think you could see that over 90 minutes today.

"I don't think we would have cared in the end if we lost and still progressed because we really wanted to get to the final, but it's even nicer this way."

For Roma, the chance to reach a second straight UEFA Europa League final after last season's defeat by Sevilla on penalties slipped away in the dying minutes of the match.

"When you manage to get it back from 2-0 down and go close to the miracle, knowing nobody has ever beaten them this season, it hurts to see us concede a goal like that. It hurts," Roma boss Daniele De Rossi said.