The London 2012 gold medallists led the world champions twice in the second half, but failed to hang on to the lead as both sides came away from the entertaining contest with a point apiece.
That proved to be a rare sight of goal in a quiet first half, and it wasn't until shortly before the half-hour mark that either side had another clear opening. Again it fell to Lozano, but this time he was denied by Timo Horn when one on one.
Michael Perez then drilled a free kick wide with 10 minutes remaining of the half, but it wasn't until after the interval that the match began to liven up.
The opening goal arrived just seven minutes after the restart when Perez turned provider, swinging a corner into the box that Oribe Peralta climbed highest to glance into the far corner, despite the efforts of the defender on the line.
Arsenal's Serge Gnabry came close to restoring parity three minutes later when he placed a shot wide of the target from inside the box, but Mexico failed to heed that warning and only two more minutes passed before Gnabry once again found himself in a good position and this time picked out the bottom corner.
Mexico were even quicker to respond to that goal, however, and within three minutes of the equaliser the defending champions had restored their advantage when Peralta's diving header struck the crossbar and fell kindly for Rodolfo Pizarro, who reacted well to scramble the ball over the line.
Things settled down a little after that run of three goals in nine minutes, but Gnabry continued to look like Germany's most dangerous player and he came within inches of levelling things up again 20 minutes from time when his effort hit the post.
Horn was called upon to make a fine save at the other end moments later before Gnabry threatened once again, only to produce a tame shot this time having danced his way into the box.
That proved to be the last of the goals as both sides settled for a share of the spoils following a frantic second half, opening their Olympic campaigns with a thrilling draw.