Hoffenheim fell to its fifth consecutive defeat and gave Frank Kramer a losing start in his job as interim coach. Kramer replaced Markus Babbel, who was fired on Monday.
Rudnevs opened the scoring in the 27th minute, heading in a cross from Dennis Diekmeier -- with the ball spinning and dipping over 20-year-old goalkeeper Koen Casteels.
Tolgay Arslan hit Hoffenheim's crossbar, while at the other end Sejad Salihovic and Roberto Firmino tested Rene Adler with long-range attempts.
Rudnevs got his sixth goal of the season in the 74th, after Sebastian Rudy's clearance fell kindly in front of him.
"We defended well, we didn't allow too many chances, it's a small improvement," said Kramer after Hoffenheim's 10th loss of the season.
With 38 conceded goals, Hoffenheim has the leakiest defense of the league.
Hamburg won despite missing midfielder star Rafael van der Vaart because of injury.
"We controlled the match," Arslan said.