When the Rolling Stones postponed the entirety of their No Filter tour this spring — including a June 4 show at Lincoln Financial Field — because of Mick Jagger’s medical condition, any hopes of seeing the band before summer was out seemed overly optimistic.

To say the least: The band’s septuagenarian lead singer needed heart surgery, for goodness’ sake. And even thinking about a still recuperating Jagger performing the only way he knows how — singing while strutting up and down a catwalk, when not motoring back and forth to either side of an oversize stage — was enough to give a nervous Stones fan a heart attack.

And yet there Jagger was on Tuesday night, along with his mates Keith Richards, Ronnie Wood and Charlie Watts — aggregate age of the four: 300 — prancing and powering through a marvelously un-slick, two-hour, rain-soaked stadium show in South Philadelphia, sounding every bit as unruly and vital as you could hope they would.

At this late stage, it’s hard not to get sentimental about the Stones — a miraculously (largely) intact entity formed in 1962 that, as Jagger pointed out, has been playing Philadelphia for “54 [blanking] years.”

That 1965 show was at the long-since-razed Philadelphia Civic Center in West Philadelphia, and the band did actually play one Pennsylvania show even earlier than that, at a Farm Show in Harrisburg in 1964.

The idea is that the Stones have been around pretty much forever, a notion Jagger underscored when he seemed to mistake the Linc for JFK Stadium, the also long-gone venue the band played when they came to town in the 1970s and 1980s.

“Most places we used to play have been demolished, and this one hasn’t,” he said, and while he was mixing up his venues, his point was germane. Buildings, eras, styles of music, and the people that play them come and go. But the Stones carry on, seemingly immortal.

Jagger’s health scare put the lie to that, of course, while also signaling that it’s past time to stand back and appreciate all that they are, while they’re still around.

The Stones would be gray-haired, were it not for hair dye. The elegant and imperturbable Watts, a jazz lover who always only plays what’s absolutely necessary and was introduced by Jagger as coming all the way “from Preservation Hall to Independence Hall,” is the only silver fox.

But in the Stones’ case, with age also comes intuitive, next-level musical communication, and the understanding that there’s little point in attempting to replicate one’s greatest hits note for note.

The Stones couldn’t do it if they tried, so they don’t bother, instead keeping their bluesy, Chuck Berry-derived snarl intact by staying raw and in the moment, unafraid that a bum note might show up here and there.

The set list wasn’t filled with rarities. Sticky Fingers’ horn-driven “Bitch,” with dual sax action from Karl Denson and Tim Ries, was the by-request song chosen by fans on the internet. And the two-song acoustic set played by only the core four at the edge of the catwalk featured “Angie” and “Dead Flowers.”

But from the opening “Street Fightin‘ Man” — the closest the Stones ever came to a political manifesto, declaring “the time is right for a palace revolution” — to the final encore of “Satisfaction,” the set was filled with warhorses that still delivered plenty of kick.

Wood and Richards weaved their uncanny twin guitars throughout the evening, with the former shining on “You Can’t Always Get What You Want,” the night’s first sing-along. In the band’s engine room, Richards and Watts played off one another, pushing and pulling the band’s shifting rhythmic foundation, keeping the sound spry.

Bassist Daryl Jones stepped out on “Miss You,” the disco-era workout that got the crowd back up out of their chairs (or rushing back from the bathroom) after a stellar two-song, Richards-sung set, including the mood piece “Slipping Away” and the delightful “Before They Make Me Run,” in which the legendary libertine remembered times when he "wasn’t looking too good, but I was feeling real well.”

And “Miss You” also was notable for achieving a measure of tenderness, with Jagger gently repeating “I miss you, girl” in a near-whispered coda as the song faded away.

Did Jagger ever show any sign of age or infirmity? Not once. Was this really a man whose health had been in serious danger just a few months ago?

There was no way you could have guessed that. His vocals were robust. Coming out on stage in a red leather jacket and black skinny jeans — and later changing into a green leather hoodie when it rained, and a top hat and floor-length coat for his Mephistopheles bit on “Sympathy for the Devil” — his peripatetic rooster dance moves are still intact, though less exaggerated and cartoonish than they once were. He’s the most fabulously fit baby boomer in the room.

He also is still a hammy, pandering, joyful showman who delights in what he’s doing. Wood, who’s an avid painter, was introduced as “the Cheesesteak Chagall.” When the band moved to the middle of the stage, Jagger referenced Philadelphia Eagles field goal kicker Jake Elliott.

And the clearly well-briefed front man might have overdone it when, with tongue in cheek, he told of driving to Wawa to get a hoagie but being waylaid by hitting a pothole. Watts was unbothered, he claimed. “Charlie gets his hoagies from Sheetz.”

Those showbiz shenanigans would have seemed merely silly, of course, if the music wasn’t in fine working order. And though not everything went smoothly — “Paint It, Black” was a little desultory to my ears — for the most part, it hummed along.

The most thrilling moments of the evening both came after the rain started to fall an hour in.

Jagger was joined at the end of the catwalk by singer Sasha Allen — who handled backup vocals all night long with Bernard Fowler — for “Gimme Shelter.” Allen wailed away on the showstopping vocal part originally sung by Merry Clayton, as the musical high drama was heightened by the meteorological conditions.

Jagger was similarly out on the edge on his own for “Midnight Rambler,” the creeping, hard-slamming blues on which he crouched down in his green leather and blew his harp for all he was worth.

And Jagger brought smiles to Watts’ and Richards’ faces when he strolled back to the main stage to lead them into a detour in the song-within-a-song of “Walkin‘ Blues.” That foundational tune for the band was sung by both Robert Johnson and Muddy Waters, the latter of whom wrote a different song that, more than 50 years ago, gave the Rolling Stones their name.

Back in 2013, before the Stones last played Philadelphia, I interviewed Jagger, and he talked about what to him “rock-and-roll is really about.” For the archetypal rock front man, it boils down to one word: “Energy. It jumps out at you, even if you haven’t heard it for ages.” On Tuesday at the Linc, watching the Stones still make that leap was a wonder to behold.