Bayer Leverkusen took a huge step towards the Europa League final after a deserved 2-0 first-leg win in their last-four clash against Roma at the Stadio Olimpico.

Florian Wirtz gave Leverkusen a half-time lead before Robert Andrich struck a superb second as the German champions proved too strong for their hosts. Xabi Alonso’s side also extended their unbeaten run to 47 games in all competitions this season.

Leverkusen, who were beaten by Roma over two legs at the same stage of last season’s competition, remain on course for the treble. They take on second-tier Kaiserslautern in the German Cup final later this month, before what now looks a likely Dublin date with either Atalanta or Marseille, who drew 1-1 in their first-leg tie in France.

Roma, who lost on penalties to Sevilla in last year’s final, had lost just three times in all competitions since the head coach, Daniele De Rossi, replaced José Mourinho in January. But after Roma striker Romelu Lukaku’s header hit the crossbar, De Rossi’s side gifted Leverkusen a 28th-minute lead.

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Right-back Rick Karsdorp’s back-pass fell short and Álex Grimaldo squared for Wirtz to sidefoot home his 18th goal of the season. Leverkusen underlined their superiority in the 73rd minute when Andrich struck a superb 25-yard shot that looped over Roma goalkeeper Mile Svilar and crept in under the bar.

Roma’s frustrations boiled over after Andrich’s strike as words were exchanged and players from both sides became involved in a melee, resulting in yellow cards for the hosts’ Leonardo Spinazzola and Leverkusen’s Granit Xhaka.

Roma were made to look second best, but did create other chances to give De Rossi hope for the return leg in Germany next Thursday. Bryan Cristante headed a second-half corner just wide and Piero Hincapie’s tackle denied substitute Sardar Azmoun, before Tammy Abraham headed over from two yards out in stoppage time.

“We fought well and showed a mature performance with a lot of discipline,” the Leverkusen head coach, Alonso, said afterwards. “We defended closely and compactly, so we are satisfied with the performance. But the return match has not yet been played.

“Overall, we played a really serious game, really professional performance,” Alonso told TNT Sports. “Not super spectacular but we did the things we needed to do. The commitment from the players has been fantastic.” The Spaniard added that defeat by Roma at this stage last season motivated his team.

“We still have this pain that it could have been better last year, and use it in a positive way – [although] this team is different and has improved a lot,” he said. “Overall, it was a very mature performance and that’s why we got a good result.”

Leverkusen could equal Benfica’s record among Europe’s top 10 leagues of 48 games unbeaten, set between 1963 and 1965, before they face Roma in the second leg. Die Werkself travel to Eintracht Frankfurt in the Bundesliga on Sunday.

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