Sevilla, Sampdoria crash out
Unfashionable Braga denied Sevilla a place in the Champions League group stage by winning 4-3 in Spain thanks to a second-half hat-trick by Lima.
The Portuguese team completed a 5-3 aggregate victory in the play-off tie to reach the group stage for the first time and leave Spain with only three representatives in Europe's most prestigious club competition.
Braga also denied Sevilla a third group stage appearance in four seasons.
Matheus gave the visitors a 1-0 half-time lead before Lima opened his account just before the hour.
Luis Fabiano and Jesus Navas hit back to make it 2-2 on the night, only for Lima to add two more goals in the last five minutes before Frederic Kanoute pulled one back for Sevilla in stoppage time.
Swiss league champions Basel won 3-0 at Sheriff Tiraspol to complete a 4-0 aggregate victory over the Moldovans while Hapoel Tel Aviv qualified with a 1-1 draw at home to Salzburg who lost 4-3 on aggregate to fall at the playoff stage for the fourth time in five seasons.
Werder, leading 3-1 from the first leg, went 3-0 down at Sampdoria before substitute Markus Rosenberg scored in the 93rd minute to set up extra-time.
Claudio Pizarro then netted as the Bundesliga team lost 3-2 on the night but qualified 5-4 on aggregate to leave Spain and Italy with only three teams in Europe's top club competition.
There was further drama as Partizan Belgrade knocked out Anderlecht 3-2 on penalties after drawing 2-2 in Belgium after letting slip a two-goal lead in the last half hour.
It is the second time Partizan have qualified for the group stage. The first time was in 2003 when they defeated Newcastle United.