Salzburg were handed a reprieve just before the half-hour mark as Moanes Dabour was fouled by Basta in the Lazio box, prompting the referee to award the visitors a penalty.
Valon Berisha stepped up and duly sent Thomas Strakosha the wrong way to draw the Austrian giants level against the run of play.
Sergej Milinkovic-Savic had a great opportunity to put Lazio ahead on the stroke of half time as he met Senad Lulic's cross in the box, but despite being unmarked, he headed wide.
Nonetheless, the Biancocelesti surged ahead in style just after the break when Marco Parolo lashed a superb backheel past Walke and into the back of the away side's net.
Salzburg went on to draw level for the second time in the match through Takumi Minamino, who latched on to Dabour's deft pass in the box to slot beyond the grasp of Strakosha on 71 minutes.
LAZIO (3-5-1-1): Strakosha; Luiz Felipe, De Vrij, Radu; Basta (Patric 65'), Parolo, Leiva, Milinkovic-Savic, Lulic; Luis Alberto (Anderson 65'); Immobile (Caicedo 85')
RED BULL SALZBURG (4-4-2): Walke; Lainer, Andre Ramalho, Caleta-Car, Ulmer; Haidara (Wolf 81'), Samassekou, Schlager, Berisha; Gulbrandsen (Minamino 70'), Dabbur