The challenge of trying to break the giant American’s serve caused Murray no end of turmoil but he kept his focus and ground out a 7-6 (11/9) 6-4 6-3 victory.
It was his sixth win from six meetings with Isner and booked a likely quarter-final spot against Frenchman Richard Gasquet, who surprisingly won the opening two sets against fifth seed Kei Nishikori.
Murray said of winning the first-set tie-break: “It was very important. It was a very close set, it could have gone either way. I got a bit lucky on the set point, just guessed the right way.
“It’s obviously difficult conditions, you don’t quite know what’s going to happen, so to go in on that rain delay ahead was very important.”
The victory means the world No 2 has reached at least the last eight at 20 of his last 21 grand slams while six appearances in the quarter-finals is the most ever by a British man.
Inevitably, the man with whom he previously shared the record was Fred Perry.
Perry went on to lift the title here in 1935, and Murray arrived in Paris clearly fancying his chances of doing the same.
His rollercoaster start to the tournament, when he might have lost to either Radek Stepanek or Mathias Bourgue, is fast becoming a distant memory.
In the third round he eased past Ivo Karlovic and, although things were a little trickier against the game’s other giant, ultimately it was a comfortable win for Murray.
Earlier in the day, Murray’s brother Jamie, and doubles partner Bruno Soares’ winning grand slam run came to an end in the third round.
The pair won the title in their maiden slam together in Australia but were unable to make it past 16th seeds Marcin Matkowski and Leander Paes in Paris.
Having won their eight previous slam matches, the British-Brazilian pair lost two tie-breaks, going down 7-6 (7/5) 7-6 (7/4).
Murray was looking to reach the quarter-finals for the first time at Roland Garros and he and Soares were the better team in the first set after retrieving an early break.
But they missed four further break points and were undone in the tie-break by veteran duo Matkowski and Paes, who have a combined age of 77.
The second set followed a similar pattern, although this time it was the Polish-Indian duo pushing the pace and they duly prevailed in another tie-break.
The defeat means Murray must wait for another chance to reclaim the world number one ranking he briefly held this spring, while his run of consecutive grand slam final appearances ends at three.