Van Persie scored 30 goals in all competitions in his first season with United, helping to fire the club to a 20th Premier League title in Sir Alex Ferguson's final campaign as manager.
"It was a genius signing, to get someone from one of your rival clubs, where he'd been [for so long] – everyone was shocked," Evans told the Guardian.
"We'd been working in training on trying to get Ashley Young running in between the right-back and right centre-back," said Evans, who now plays for Leicester.
"There was a moment where Robin caught everyone out and tried a reverse pass with his right foot, into Ashley's path.
"Branislav Ivanovic ended up getting sent off for being the last player [when fouling].
"To be able to carry out this kind of plan made Robin the manager's dream.
"There are other moments that stand out, too. His goal against Arsenal in his first game against them at Old Trafford – he did so with his right, and you think: 'This guy can score'."