Rodriguez missed all of last season with a cruciate injury suffered in April 2014, but the England striker is now fit and on Saints’ pre-season tour of Austria.
And he marked his return to the pitch with two close-range finishes – one with his left foot, the other with his head – to add to goals from new signings Juanmi and Cedric Soares.
Their German opponents, who are ahead in pre-season, ran out narrow winners, but Ronald Koeman was happy with his side’s first friendly outing.
He told the club website: “I’m happy about the minutes and the physical game what we had. We scored some great goals and the positive things were two goals and the first 45 minutes of Jay.
“It was his first 45 minutes and he did well. He scored two good goals. That gives everyone a positive feeling about tonight and for sure the same for Jay.
“Also we had the first goal of Juanmi, the first goal of Cedric Soares. A lot of positive things, and the result is not the most important.”