Greig Laidlaw kicked four penalties to ensure Scotland built on their Round 2 hammering of Italy despite Ulster wing Craig Gilroy scoring the only try of a match which Ireland will feel aggrieved not to have won.
For Johnson, it evoked memories of the 'rope-a-dope' technique employed by three-time heavyweight king Ali when he withstood a barrage of blows from the heavyhanded Foreman to somehow knock out the champ in the eighth round in Zaire some 39 years ago.
"At half-time I was thinking that it was like Ali versus Foreman, lulling them into some false sense of security," said Johnson.
"My neck was sore looking down one side of the pitch!
"We took our opportunities and they didn't take theirs - that was the sole difference.
"I've been on the other side of games like that. England were a quality side that punished us; Ireland didn't punish us.
"We had a massive penalty count against us and massive territory against us, but we fought, and while we missed some one-on-one tackles, the recovery of those was fantastic."
Johnson was quick to point out his pride in the workrate and commitment of his entire squad as their togetherness and tenacity saw them keep their hopes of a first Championship title since 1999 very much alive.
The Australian insists there is still plenty of improvement to be made and that there is no chance of the Scots getting carried away, but he admits glory is within reach as they prepare to for a home tie with Wales in a fortnight.
"We're still in the tournament - we are in it up to our ears. That's great for the fans and the team but let's not get carried away," added Johnson.
"They'll be hurting, we'll enjoy the next 24 hours, but if we want to be a good quality side we've got to acknowledge that we have to work on some things.
"Ireland scored after half-time and I thought, 'here we go, this is a test' and we fought back, it says a lot about this group.
"There wasn't much to like as a rugby coach, but a lot to like as a person. Let's put our qualities together with the character we showed.
"When we get things right we can hurt sides. We've lost a lot of possession and territory in the first three games, but that brought out the blue-collar boy in me. We had a wry smile, but there was great heart with it."