Sevilla also moved on from Group H even though it conceded a 90th-minute equalizer at home to Portuguese side Estoril in a 1-1 draw.
Lazio, Genk, AZ Alkmaar, POAK, Rubin Kazan, Trabzonspor, Anzhi, and Ludogorets Razgrad also qualified for the knockout rounds with one group game to go.
Beside the 24 teams to emerge from the group phase, the eight teams that finish in third place in their Champions League groups will also join the next round of Europe's second-tier club competition.
Valencia's Parejo put in a deflected attempt by Juan Bernat after Swansea goalkeeper Gerhard Tremmel punched out a corner to grab the lead for good in the 20th minute.
Sevilla had a bright start seven minutes in when Jose Antonio Reyes sparked a lightning attack with a pass for forward Kevin Gameiro to hit on the break.
But Estoril won the ball in the second half and pressed Sevilla into its box until a short delivery from Javier Balboa led to Ruben Fernandes squirting a shot under goalkeeper Javi Varas on the brink of stoppage time.
"We played well in the first half, but then we relaxed and paid for it," Reyes said.
Freiburg's 2-1 win at Liberec means that it can qualify by beating Sevilla in the last round.
In Lyon, forward Bafetimbi Gomis tapped in a squared ball from Yoann Gourcuff in the 66th to down Betis.
Tottenham had already been guaranteed the top spot in its group when Russian club Anzhi could do no better than a 1-1 draw with FC Sheriff. The draw was also good enough to send Anzhi though.
But the English side played through sub-zero temperatures and a dusting of snow at its northern Norwegian hosts to extend its winning run.
Tottenham went ahead in the 63rd when defender Vlad Chiriches got a touch on a cross from Gylfi Sigurdsson, sending the ball off Causevic and into the net.
Dembele scored his goal after receiving a pass from Sigurdsson near the penalty spot, where he fired into the left corner.
Turkish team Trabzonspor and Lazio both advanced after comfortable wins. Trabzonspor only needs a draw to with Lazio in their final meeting to finish first in Group J.
Olcan Adin was the night's leading scorer with a hat trick to lead Trabzonspor to a 4-2 win over Apollon, while Lazio won 2-0 at Legia Warsaw after goals by Brayan Perea and Felipe Anderson. About 120 Lazio fans were detained before the match after attacking police vans, authorities said.
"This victory has given us a lot of self confidence," said Lazio's Lorik Cana. "We are in good position. If we win our last game, we have a chance to win the group."
Rubin Kazan advanced from Group D after drawing 1-1 with Maribor.
Ludogorets Razgrad won Group B by handing 10-man PSV a 2-0 loss at home.
Eintracht Frankfurt claimed first place in Group F by beating Girondins Bordeaux 1-0 on the road.
Genk's comeback 3-1 win to beat Dynamo Kiev earned it top spot in Group G.
