It also matched Cole's record for the most goals scored by a player in their first seven PL matches for Man Utd.
But Lukaku's consistency has him closing in on another Cole feat.
Saturday's victory was the sixth different match in which Lukaku has scored this season, putting him on course to break the record for the most matches scored in during a Premier League campaign.
But both totals were posted before the competition was cut to 20 teams.
Lukaku has only failed to score in one match, against Leicester City in Matchweek 3.
If he keeps up his current rate the Belgian will end 2017/18 having scored in 32 different matches, 11 more than Ronaldo and Van Persie.
|Player||Season||Club||Matches scored in|
|Robin van Persie||2012/13||MUN||21|
Liverpool will be the next opponents to try to slow him down when United visit Anfield on Saturday 14 October.