The 25-year-old netted twice – both times from the penalty spot – as the Red Devils had to work hard to earn a 2-0 victory in Bucharest to move his career tally to 26 goals.
The achievement moves him past former team-mate Paul Scholes in the standings, while Premier League rivals Frank Lampard of Chelsea and Liverpool captain Steven Gerrard remain close behind.
Rooney’s first goals in Europe’s elite club competition memorably came on his debut for United after signing from Everton in 2004. Then just 18, Rooney scored a hat-trick against Fenerbahce as his new side romped to a 6-2 win at Old Trafford.
Now in his eighth season as a United player, the England striker’s biggest goal in the competition came in last year’s final at Wembley, where he levelled the match against Barcelona before being unable to prevent a 3-1 defeat on the night.