The Brazilian midfielder opened the scoring after 21 minutes at the Mercedes-Benz Arena before Nigerian Onazi doubled the Serie A side’s advantage after the break.
Lazio are now odds-on to see out the result on home turf next week in Rome and advance to the quarter-final stage.
Tottenham Hotspur trounced a sorry Inter Milan 3-0 while last year's European champions Chelsea were humbled 1-0 by Steaua Bucharest after being stung by a Raul Rusescu penalty.
Big-spending Russian pair Zenit St Petersburg and Anzhi Makhachkala failed to manage a goal between them. Zenit lost 2-0 to late goals at FC Basel and Anzhi were held 0-0 by Newcastle United.
Zenit were also goalless until the last 10 minutes at Basel, then Chilean midfielder Marcelo Diaz scored from close range for the Swiss champions.
Veteran Alexander Frei converted a stoppage time penalty for a foul on Mohamed Salah by Luis Neto, who was also sent off.
Former European champions Benfica beat Bordeaux 1-0 thanks to an unlucky own goal and Fenerbahce won 1-0 at Czech side Viktoria Plzen while the Levante-Rubin Kazan tie finished goalless.
Benfica edged Bordeaux thanks to an unlucky own goal by Cedric Carrasso, Rodrigo's shot bouncing off the crossbar and hitting the visiting goalkeeper to ricochet into the net.
Cameroon forward Pierre Webo scored an 81st minute goal to give Turkey's Fenerbahce a 1-0 win at Plzen.
