Mercedes driver Hamilton and Red Bull rival Verstappen have shared the top-two finishing positions in each of the opening three grands prix so far.
Hamilton's 97th F1 career victory in Portugal on Sunday means he holds an eight-point cushion over Verstappen who salvaged second from a tricky weekend for the team given the car did not appear to suit the track.
The seven-time F1 champion still had to fight his way past Verstappen and team-mate Valtteri Bottas to secure the win, which impressed F1's managing director motorsports Brawn.
"Lewis was his usual imperial self in Portugal, pulling off brilliant – and ultimately crucial – overtakes on both his team-mate Valtteri and main title rival Max to clinch victory," said Brawn in his regular post-race column.
"He really had to work for the win and it was a fine example of how the consistent challenge that is emerging from Red Bull and Max is pushing Lewis to another level.
"Lewis may have faced major opposition from his team-mate over the last few years, but he’s not had to contend with a threat from outside, and so far, he is responding as a seven-time world champion would."
Brawn, though, also feels Verstappen is showing a different side to his racing character that has arguably not been seen previously due to the fact he is firmly in the hunt for the title as he is being forced to play the long game.
"It’s clear Max is approaching this championship in a different way because he finally has a title-winning car," added Brawn. "His mindset has changed and he’s got an eye on the whole championship.
"And it had to change because when you’re a title contender, the focus has to be on consolidating when you’re not the fastest and when opportunities such as a mechanical issue for a rival or a safety car present themselves, you must be in a position to strike.
"If Lewis had had an issue or Mercedes made a mistake in Portugal, Max was in a position to react, so while it was frustrating for him, he can see Red Bull are responding and he accepts that there will be an ebb and flow to this championship.
"We’ve had three races on three different tracks and on each, there has been a proper fight between Max and Lewis, which bodes very well for a fascinating title battle this year."
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