Rivaldo completed a hat-trick with a stunning overhead kick a minute from the end of Barcelona's final league game against Valencia to earn the Catalans a 3-2 win and a place in the Champions League next season.
Rivaldo's fourth-minute free kick and a second goal just before half-time was twice equalised by Baraja in the 26th and 47th minutes, before Rivaldo brought the house down with a superb overhead kick in the 89th minute.
Valencia, having lost in the European Champions League final this season for the second successive year, now have to make do with UEFA Cup football next season. Celta Vigo, who drew 1-1 at Real Zaragoza, earned a second UEFA Cup spot, and seventh-placed Villareal might even sneak another berth through the back door if either Celta Vigo or Barcelona win the Spanish Cup, currently at the semi-final stage.
The Spanish second division matches also finished yesterday and Real Betis and Tenerife join Seville, already assured of promotion, in the top flight next season.
Real Madrid had secured their 28th title and their first since 1997 two weeks ago and Deportivo La Coruna and Real Mallorca had already sealed their Champions League spots.
Just on Wednesday, Barcelona lost the Catalan Cup to a third division side and, needing a quick pick-me-up, Rivaldo did not take long to oblige.
He curled the ball round Valencia's wall to put Barcelona in the driving seat.
Midway through the half, Barcelona almost scored again when striker Simao hit the crossbar following a cross from the left by Dutchman Marc Overmars. Moments later in the 26th minute, Valencia were level. Unmarked Baraja headed home a corner from the right to starkly highlight Barcelona's defensive frailties which have hampered them during the season.
Once more Rivaldo got Barcelona out of trouble with a goal out of the blue. About 25 yards out in the centre of the pitch, he unleashed a powerful left foot shot which beat the keeper for sheer speed.
Valencia wasted no time getting another equaliser. Baraja scored with a free header after a cross from the left moments after the break to keep them on track.
Patrick Kluivert, who had little success most of the night, was in a good position 15 minutes from time when Overmars fed him from the left but his first touch let him down and the opportunity was missed.
A Rivaldo free kick on the edge of the box went begging before the stage was set for the 1999 FIFA world player of the year to score with a superb goal.
Overmars played the ball through to Rivaldo who controlled the ball on his chest with his back to goal. As the ball came down, Rivaldo hit an overhead kick with his left foot into the net to leave the demanding Nou Camp fans celebrating. Real Oviedo were relegated after a 4-2 defeat at Real Mallorca.
That result, coupled with a 1-0 win for Osasuna at Real Sociedad, saw Oviedo slip to 18th in the table and sent them down along with Numancia and Racing Santander.
Oviedo needed just a point to be certain of keeping their place in the first division but their task was complicated by the sending-off of Frank Rabarivony nine minutes before half-time.
