Five-time European champion Liverpool beat Toulouse 4-0 to complete its qualification for the group stage of the Champions League on Tuesday.
Netherlands striker Dirk Kuyt scored twice in the last three minutes for Liverpool, which lost last season's final 2-1 to AC Milan. Earlier goals by Peter Crouch and Sami Hyypia added to a 5-0 aggregate win in the third-round qualifying matches.
The Reds will be joined in today's draw for the lucrative group stage by Lazio and Rangers.
Lazio won 3-1 at Dinamo Bucharest to round off a 4-2 aggregate victory. Rangers beat fierce rival and Scottish champion Celtic into the group stage by drawing 0-0 at Red Star Belgrade to complete a 1-0 win.
Sevilla, which has won the last two UEFA Cups, was set to play AEK Athens but the match was postponed until Monday because of the death of Sevilla midfielder Antonio Puerta.
Liverpool already led 1-0 through Andriy Voronin's goal in the first match two weeks ago and went close to extending its lead through a third-minute shot from a free kick by John Arne Riise, but the shot was saved by Toulouse's goalkeeper.
Crouch, who has not started a match in Liverpool's unbeaten start to the Premier League season, put his team ahead on the night in the 19th. The England striker flicked in Kuyt's cross to the far post with the outside of his right boot.
"It was important to get through to the next round, but it was nice for me to get my first goal of the season," Crouch said.
"It was important we started the season well," he said. "If we progress the way we've started, we're looking good."
Hyypia, who was captaining the home side in the absence of the injured Steven Gerrard and Jamie Carragher, stretched the advantage in the 49th with a header.
Kuyt then completed the victory with a low shot in the 87th and a flick over the 'keeper in injury time.
Lazio's place in the competition was in doubt after it drew 1-1 at home two weeks ago. The Italian side's chances looked even bleaker when it trailed on Florin Bratu's 29th-minute goal.
However, two second-half goals by Tommaso Rocchi and one by Goran Pandev carried Lazio into the group stage, where it will join Italian rivals Inter Milan, AC Milan and AS Roma.
Rangers made it through to the draw after goalkeeper Allan McGregor made two key saves on shots by Igor Burzanovic and one from Ognjen Koroman to preserve the visitor's aggregate lead.
The Serbian champions were unable to solve a defense protecting a 1-0 from two weeks ago.
Rangers had two chances in the second half, but Jean-Claude Darcheville's shot flew past the left post and Lee McCulloch's low shot was saved by goalkeeper Ivan Randjelovic.
Half the 32 places in the group stage are already filled by sides including the winners of Europe's top national leagues.
Four-time European champion Ajax is the high-profile club most at risk of elimination in the qualifying rounds. The Dutch club trails 1-0 ahead of its match at Slavia Prague.
Two-time runner-up Valencia holds a 3-0 lead going into its home match with Elfsborg, while former winners Celtic and Benfica are also in action.