The Bavarian giants had to do it the hard way, recovering from an early setback to climb back above RB Leipzig and into top spot on goal difference in the table.
Robben ensured that there was to be no looking back for the visitors from that point on, the Dutchman adjusting well to head home with just short of a quarter of the game gone to put his side into the lead.
Prior to that key second goal for the Bundesliga champions, Thomas Muller shot straight at Lossl to see his wait for a goal continue, but Robben in particular was growing more and more into things.
The Dutchman should have done better when played in over the top on the hour, only for a heavy touch to let him down as Lossl raced out to pounce.
With just the one goal in it Mainz always felt that they had a chance of nicking a point, and that nearly proved the case when Levin Oztunali came close to taking advantage after a corner was not dealt with in the visitors' box.
Carlo Ancelotti's men made certain of the points in added time, however, thanks to Lewandowski's second of the evening via a well-struck free kick into the top corner from the edge of the box.