After claiming his historic 100th pole position on Saturday, Hamilton quickly lost first place on the run down to turn one at Barcelona's Circuit de Catalunya.
The seven-time F1 champion then spent the following 24 laps staring at the back of Verstappen's Red Bull as he maintained a steady gap of around one to 1.5 seconds before making a two-stop strategy work to perfection to land his 98th victory.
"I’m continuing to love this battle we are having," said Hamilton, who has opened up a 14-point gap over Verstappen in the drivers' standings.
"I didn’t know whether we would be able to follow them as closely as we did in the end. Obviously, turn one, the start was not ideal and we are going to have to review it and see how we can do better in the future.
"But as soon as we got passed in turn one, I was like, ‘Okay, switch into a different mode’.
"It was actually a really good day. I learned a lot about Max, perhaps more than all the other races put together. This has been a good one in that sense."
Asked to expand on his remark, Hamilton added: "When you are with people on track you get to see different things and watch closely.
"Obviously, I was following relatively closely and I learned a lot about his car and how he uses it, so it was a good race in that respect."
After Hamilton's second stop with 24 of the 66 laps remaining, the 36-year-old was left chasing down a 23-second gap to Verstappen which he completed with six laps remaining.
Although Hamilton had questioned in his own mind the strategy in the race, he soon dismissed them and placed his trust again in the pit wall and team back at Brackley.
"Great, great teamwork from all of us," enthused Hamilton. "We were here until late most evenings discussing strategy, and we had all the bases covered in that respect.
"Of course, it just meant that I had to do the job on track. Coming back from 20-odd seconds wasn’t easy but I think it [the strategy call] was the right one in the end."
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