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Norris was fourth in Azerbaijan last weekend to close the gap on title rival Max Verstappen by three points.
The pair are now separated by 59 points with seven races to go.
Meanwhile, Piastri won the race in Baku, his second win of the season, and is the highest-scoring driver across the last 11 races.
His victory last weekend came after a stunning performance and with an important contribution from Norris.
Having not pitted, the Brit held track position ahead of Sergio Perez, who had boxed and posed an undercut threat to Piastri.
Instructed by the pit wall to do what he could to delay the Red Bull Racing driver, Norris slowed through the middle sector of the lap, ensuring his team-mate emerged from the pit lane still ahead.
It was a crucial moment as it allowed Piastri to attack then-leader Charles Leclerc, and ultimately seize the race lead.
The exchange also highlighted the way McLaren’s much derided employment of team orders works in realty.
“Lando is obviously still ahead in the championship and, just being honest, he has a more realistic chance of winning the drivers’ championship,” Piastri said of McLaren’s use of team orders.
“But I think the race in Baku was honestly a great exhibition of how we want to go racing as McLaren.
“Lando was definitely a factor in helping me win the race in Baku by some ‘tyre saving’ with Checo.
“Those kinds of things are the message we’re trying to get across and I think Baku, we got it across perfectly on track; our culture and how we want to go racing.”
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Norris needs to reel Verstappen in, on average, by more than eight points a weekend until the end of the season if he is to become champion.
That will require big points finishes at events where Verstappen fails to fire – the three points he scored over the Dutchman in Azerbaijan was, in reality, a loss.
While Piastri will work in support of Norris when necessary, he remains free to fight for victories for himself if they’re available.
“If I’m in a position to still win races, then that’s what I want to do, and I think I showed in Baku that I’m capable of doing that,” Piastri noted.
“But naturally, if there’s times where I can help out for Lando’s championship bid, then I’ll be happy to help out as well.
“It’s not really changed anything,” he added of his Azerbaijan win and its impact on team orders.
“I’m still free to go into every weekend trying to achieve the best result and there are so many situations…
“There was obviously a lot of talk before Baku and after qualifying, there was no talk because we were so far apart on the grid.
“So until you arrive in specific situations, difficult to discuss, apart from demonstrating it on track.”
McLaren will don a tweaked livery this weekend with white panels adorning its sidepod and engine cover.
The change is in deference to sponsor OKX, continuing a recent trend of Singapore design changes for the squad.
