Named in the same team as van Persie for the first time, Wayne Rooney created both goals in the Group H encounter in Romania on Tuesday night.
And the winner, four minutes after the break was simply sensational as the 29-year-old took his tally to six for his new club.
The result means back-to-back wins over Braga will take United into the last 16 with two games to spare.
However, Sir Alex Ferguson cannot be entirely happy with this trip to Transylvania, and was left spitting blood as his team fell behind for the sixth time in nine games.
The Scot could not have made his position any clearer either when he delivered his forceful pre-match address on Monday night: "It will be the last".
It was a direct ending to being quizzed about his side's woeful record of conceding the first goal.
But after 14 minutes, staring down at him to his left from an otherwise pitch black sky, there it was again. Cluj 1 Manchester United 0.
And whilst the Romanian champions could congratulate themselves on the effectiveness of the counter-attack Ferguson had primed his side for, from United's point of view it was all rather disappointingly simple.
Rafael Bastos swept a superb pass out wide to Modou Sougou, who exposed Patrice Evra's defensive frailties, then whipped in a low cross which Kapetanos finished in fine style.
Speaking to ITV before the second half began, Ferguson branded it "an absolute shocker".
It is fair to assume his assessment within the confines of United's dressing room was not quite as measured and for a short while afterwards, the visitors looked nervy and uncertain.
Rooney dropped ever deeper in search of possession, which, considering he was starting behind the front two, took him virtually in front of United's defence.
The visitors good fortune came in the departure of Sougou through an injury that cost Cluj much of their attacking zest.
And within five minutes, United had taken advantage.
Van Persie had already come agonisingly close to levelling when he latched on to an inspired Tom Cleverley lofted pass.
But when Rooney floated over a free-kick from the left, United enjoyed their second slice of luck.
Had van Persie made a firm contact with his header, Mario Felgueiras might well have saved.
Instead, the Cluj keeper was committed when the ball looped off Van Persie's shoulder and was helpless to prevent it dropping over him into the net.
It was the former Arsenal man's 19th goal in 49 Champions League appearances. His 20th arrived four minutes after the re-start.
There was no luck involved this time. This time it was pure class.
Again Rooney was the provider. On this occasion the delivery came from the right.
Stationed in a central position about eight yards out, Van Persie watched the ball drop, then steered it into the bottom corner with a delicate touch of his left foot.
It was the kind of sublime moment Ferguson was buying when he persuaded the Glazer family to splash out £24million on a player with relatively little resale value in the summer.
The noisy - if respectful - home fans thought they were celebrating an equaliser as they rose to acclaim Cadu's goalbound effort.
But not for the first time in his short United career, David de Gea's athleticism got his team out of trouble as he repelled the Cluj skipper with a magnificent reaction save.
Van Persie came close to completing his second Red Devils hat-trick when he slid in to reach yet another Rooney cross. This time, though, he could not quite get there.
Scott Wootton was introduced for his European debut 11 minutes from time, after which the visitors needed to survive only one scare when De Gea pushed Bastos' diving near-post header behind.
In pure results terms, Ferguson has got exactly what he asked for after last season's group stage debacle.
However, the 70-year-old will be acutely aware he must find a remedy for those bad starts if United are to stand any chance of winning silverware this term.