Wellington sit in second place with three games remaining.
His go-ahead penalty was his 39th goal for the German club this season and 15th against Arsenal in his career.
The rivals are the last two teams to win the European club trophy.
The NZ women had beaten their rivals 4-0 three days earlier.
The Merseyside club have dropped further down the ladder.
The midfielder is hanging up her boots after a 166-game career at senior level.
Chris Wood has now found the back of the net in four consecutive matches.
Liverpool move back to second but have a game in hand.
The result moved the Mariners ahead of the Phoenix at the top of the table.
