It was Rolfe's second straight start for the Danish Superliga club. On Saturday, in his first start for AaB, Rolfe recorded an assist in a 2-0 victory over AGF. Wednesday's win lifts AaB into fourth place and four points behind OB.
Rolfe joined AaB at the beginning of the year during the Danish Superliga's winter break. He initially had trouble breaking into the starting 11, but the former Chicago Fire standout appears to have secured his spot with six games remaining in the regular season.
Yura Movsisyan also earned a game-winning strike in the Danish top flight on Wednesday.
The former Real Salt Lake forward scored two first-half goals in Randers' 3-1 win at Silkeborg, taking his scoring tally for the club to three.
Randers is now just two points away from climbing out of the relegation zone in the 12-team division, having begun the second half of the season an incredible 14 points adrift from safety. Since Movsisyan joined in January, the club has not lost in nine outings and is unbeaten in 11 games since November.
Also in Danish Superliga action, United States midfielder Benny Feilhaber went 90 minutes and earned a yellow card in AGF's 1-0 road loss to Midtjylland.