Lazio beat Zenit St Petersburg 3-1 in the Champions League on Tuesday.
Immobile, who missed the previous two Champions League games because of positive COVID-19 tests, fired Lazio in front after three minutes and converted a penalty early in the second half as he took his tally to three in three group games.
The win took Lazio, who are in the group stage for the first time since 2007-08, within touching distance of the last 16. They stayed in second place with eight points from four games, a point behind Borussia Dortmund and four clear of Club Brugge.
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Zenit are bottom with one point and out of contention.
Lazio were quickly off the mark when Immobile, Serie A's top scorer last season, collected Lucas Leiva's pass with his back to goal and scored with a powerful shot on the turn.
Parolo, who had not played in the Champions League group stage before this season, scored with a low shot from outside the area in the 22nd minute after Joaquin Correa broke down the left and pulled the ball back.
Artem Dzyuba pulled one back for Zenit three minutes later with a shot on the turn and Aleksandr Erokhin missed a chance to equalise as the game briefly threatened to slip from Lazio's control.
But, after several missed chances, the hosts restored their two-goal lead 10 minutes after the restart when Wilmar Barrios' reckless lunge on Immobile led to a penalty which the Lazio forward fired past the helpless Mikhail Kerzhakov.
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