After a driveshaft failure in qualifying relegated Verstappen to starting 15th in Jeddah, the two-time world champion climbed the order in the race but had to settle for second behind team-mate Perez, who had a free run to pole.
That means Verstappen and Perez head to Australia with one win each and just one point separating them in the standings - with Verstappen grabbing the fastest lap bonus point on the final lap of the Jeddah race, taking it off Perez in the process.
While Perez proved a reliable asset for Red Bull over the past two years, he didn't manage to put Verstappen under regular threat. But speaking to Autosport, Hill believes the Mexican will be offer more resistance this year.
"Checo knows what he's up against, but he's not going to go down without a fight. It could be quite interesting," said 1996 F1 world champion Hill, who is heading to Melbourne as part of the Ten Network's F1 coverage in Australia.
Amid expectations that Verstappen will soon assert his dominance on track as he aims to score a hat-trick of world titles, Hill reckons the Dutchman and his clan will also be exerting pressure off track where necessary.
"I think the problem that you have is that Max is a bit of a force of nature, and it's how much pressure he can put on the team to make sure his championship aspirations are not interfered with by Checo," said Hill.
"From the point of view of the sport, I think that they need to let Checo have every opportunity to fight with a level playing field within that team. Because I know the pressure from the Verstappens, his dad as well, on Red Bull will be intense.
"He'll be pulling out the card of saying, 'I'm your future. The whole opportunity is built around me' and he'll be leveraging them."
Hill praised Perez's ability to come into Red Bull as Verstappen's team-mate and gain a foothold, which his less experienced predecessors Pierre Gasly and Alex Albon didn't manage to do.
"We've seen young guys go there and find themselves without friends and they can be intimidated, and they've had to go elsewhere, like Gasly and Albon," Hill added.
"You could even say Mark Webber and Daniel Ricciardo have experienced that. It's a tough environment, Red Bull. They don't put their arm around you and go, 'we'll look after you, don't worry'.
"Checo has got people in his corner and we'll see how it plays out.
"Whatever happens, the Verstappens won't be taking it lying down. You saw after Saudi Arabia that Max was... I would say sulking is not too strong a word. He looked very unhappy about the way things went. They don't like coming second."
