The Finn had led the opening phase of the race at Imola on Sunday, but was pitted in response to the pursuing Max Verstappen moving first to change tyres.
While Bottas had to cover Verstappen to avoid getting undercut, Hamilton asked to stay out and pulled a very long stint on the medium tyres.
That long run in doing a different strategy gave Hamilton the time gap he needed to pit and stay ahead of Bottas – and his plight was made much easier by a brief Virtual Safety Car period that minimised the time lost when he pitted.
Hamilton's green light to run a different strategy appeared to be in contrast to recent decisions where Bottas was not allowed to take different tyre compounds in his duels with the world championship leader.
But Bottas is clear that what happened at Imola was above board, and that the team had been clear that, in fighting Verstappen, the Mercedes drivers would likely diverge on strategy.
Asked about the contrast between Hamilton doing something different and him being forced recently to stick to the same tyre compounds, Bottas said: "It was two different scenarios, I would say.
"We went through the plans [on race] morning, and what happens if one of us gets under pressure and there's a possibility that Red Bull could undercut.
"That was me, so obviously I had to react and it would have been the same case if I was in Lewis's position, that the only thing I would want to do is to go long and seek the opportunities.
"It really paid off for Lewis and, if we were the other way round, it would have been the same for me."
The gains that Hamilton was able to make were amplified by Bottas being hobbled by damage he had picked up after striking a piece of debris from Sebastian Vettel's front wing endplate.
Although the VSC guaranteed Hamilton could jump both Bottas and Verstappen, Mercedes reckoned that things would have been extremely tight without it.
Asked how close it would have been if Hamilton had not had the help from the VSC, track engineering director Andrew Shovlin said: "Extremely close. There were times where Lewis just had the gap but he had the gap by half a second or so.
"But the problem is you're dropping him out on hard tyres and they have got a warm-up curve, and that means that they're down by a second or a second and a half.
"While he looked like he could build it, we didn't really want to sort of have him dropping into that fight with Valtteri and Max on cold tyres if we could actually get the gap.
"So he was sort of getting towards having it, and then obviously the VSC came out which just made it quite an easy situation for him to deal with."