Lawson crossed the line six-tenths ahead of Tsunoda, holding off the more experienced driver while a DRS train including Lando Norris and Lewis Hamilton closed in behind him.
Even with Tsunoda on fresher tyres, Racing Bulls made it clear there would be no orders to yield.
“There were none at all,” Racing Bulls sporting director Alan Permane told DAZN.
“We weren’t going to let him through, of course. Liam did a great job keeping behind a faster car.
“Yuki had fresh medium tyres and Liam did a great job holding him off with elbows out. Liam is very tough mentally, very strong.
“He’s been focused all weekend. He drove perfectly.”
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Lawson said the final laps were intense as he focused on defending his position.
“I had no idea what position I was in until we crossed the line, but I knew we were in a decent position because of all the cars that were behind me,” he said.
“At the end of the race, obviously, I’m going to try and take a bit more risk to keep it there.”
The Kiwi had started from a career-best third on the grid, following a chaotic qualifying session that featured a record six red flags.
During the race, George Russell moved ahead of him during the pit stops while Kimi Antonelli overtook him on track, but Lawson held off Tsunoda and the cars behind to finish fifth — marking his best-ever result in Formula 1.
“I think [it was] rewarding after the last 10 or 15 laps, it was pretty intense,” Lawson reflected.
“Obviously, it is a little bit disappointing from where we are starting and realistically we didn’t have the speed to fight with the guys in front today. But you’re always hopeful.
“And we tried everything today, but there just wasn’t quite enough, but still to have a P5 is big for us, especially in the Championship right now.”
Lawson said he was looking forward to maintaining consistency that helped deliver his standout weekend in Baku as he enters a stretch of circuits with prior F1 experience.
“The main thing is, as I say, our car has been consistently good across the board at all sorts of different tracks, so that’s very positive for us,” he added.
“Going forward, we need to try and keep that consistency and try to find a little more where we’re fighting for very good results.
“We didn’t quite have the speed for Williams [in Baku], but to finish where we did, if we can consistently do that, it’s very strong for us.”
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