Captain Eden Hazard opened the scoring for Roberto Martinez's side in the 17th minute after Lukaku's shot had been blocked, before Mexico levelled through Andres Guardado's penalty after 38 minutes.
Lukaku grabbed his first shortly after half-time, only for PSV Eindhoven midfielder Lozano to take centre stage with an impressive double.
His first was a cool finish from outside the area and his second was a superb first-time volley after Thibaut Courtois had saved his initial shot.
Lukaku was to have the final say, though, as he grabbed his second 20 minutes from time to ensure the game finished level.
Mexico started in purposeful fashion and came close to taking the lead inside the opening five minutes as Miguel Layun's swerving drive from distance was palmed away by Courtois.
Belgium started to exert their authority soon after, though, and were rewarded with the game's opening goal.
Hazard picked up the ball just inside the Mexico half and set off on a surging run that ended with a smart pass into the feet of Lukaku.
The Manchester United forward's thumping effort was parried away by Guillermo Ochoa, but only as far as the onrushing Hazard, who had the simple task of stroking home from six yards out.
Mexico levelled seven minutes before the break and it came from a miserable piece of defending by Laurent Ciman.
The Montreal Impact defender brazenly tugged back Javier Hernandez as the West Ham striker tried to latch onto a cross and Guardado coolly slotted past Courtois from the resulting spot-kick.
Hazard's effort from an acute angle was kept out by Ochoa soon after, while the influential Kevin De Bruyne saw a shot crash off the outside of the post as the Red Devils tried in vain to retain the lead before the break.
The second half started at a frenetic pace, with Lukaku scoring his first in the 55th minute. Substitute Dries Mertens did well to create space down the right and clip in a cross that the 24-year-old managed to get his thigh to from close range.
Their lead lasted less than a minute, though, as Lozano scored the first goal of his quick-fire brace.
The 22-year-old expertly pulled a long ball out of the sky before firing a half-volley inside the right-hand post.
His second, just four minutes later, was even better. His initial shot from the edge of the area was pushed back towards him by Courtois and he responded by unleashing a thumping first-time volley past the Chelsea goalkeeper.
A familiar combination teamed up for Belgium's equaliser in the 70th minute as the lively Mertens crossed from the right for Lukaku to clip a delicate finish over Ochoa to level the scores again.
Lozano squandered a glorious opportunity in the closing stages to grab a memorable hat-trick and win the game for Mexico, but his effort skewed agonisingly wide of the far post.