The race featured two safety cars and a red flag.
After starting tenth, Lawson equalled his best ever F1 result while team-mate Arvid Lindblad finished just behind him after starting 15th on the grid.
"For us it's a good result, it feels really good especially where we started the weekend and obviously where we started the race as well," Lawson told Sky.
Lawson and Lindblad were lucky to get to the grid as the Racing Bulls team were still working on both cars in the pit lane just before the start.
Both drivers made their way through the field as the chaos went on around them with seven drivers failing to finish while others are still under investigation for a variety of infringements.
Lawson is now ninth in the Drivers Championship with 26 points.
However he admitted he had doubts about his race today.
"I didn't think I was going to race, I turned up to the garage and we had issues and I saw the car in pieces and so to put it together and just go and have a car that was very competitive was great."
Antonelli built a commanding lead after starting from pole in his Mercedes but that evaporated after a late red flag to inspect a crumbling surface at the final corner following a crash that took out Ferrari's Charles Leclerc.
After a delay of around 40 minutes while repairs were carried out, the race resumed with a standing start but 19-year-old Antonelli remained unfazed as he became the youngest ever winner of the iconic race.
Ferrari's Lewis Hamilton was runner-up for the second successive Grand Prix with Red Bull's Isack Hadjar provisionally third, although he was one of a number of drivers under investigation for a variety of infringements.
Max Verstappen, who lined up second on the grid, stalled at the start and retired after one lap. McLaren driver Lando Norris also retired with mechanical issues.
Hamilton, who equalled the late Ayrton Senna's eight Monaco podiums, moved above Antonelli's team mate George Russell into second place in the standings, 66 points behind Antonelli.
The next round is in Spain.
- RNZ/Reuters
