Bundesliga: Augsburg 0 Hamburg 2
Rudnevs set up Hamburg's first-half opener and then took advantage of a fine pass from Rafael van der Vaart to score his team's second goal midway through the second period.
Having lost 1-0 at home against Stuttgart last week, Hamburg got back on track with a win on Friday, although Augsburg could feel disappointed they did not get at least a draw having done most of the attacking throughout the match.
Augsburg had 19 shots to 11, earned 13 corners to three and crossed the ball 23 times to seven but poor finishing meant the hosts failed to get on the scoresheet for the second game in a row, having drawn 0-0 away to Nuremburg last week.
Too few of the shots from Augsburg players tested visiting goalkeeper Rene Adler and Hamburg made them pay in the 13th minute.
Rudnevs fed Heung-Min Son on the right-hand side of the penalty area and the 20-year-old Korean winger took a touch inside and curled his left-footed shot inside the far post to put Hamburg 1-0 ahead.
Hamburg extended the lead in the 63rd minute when a nice exchange of passes on the edge of Augsburg's area culminated in Van der Vaart sliding the ball to Rudnevs, who got free inside the area and smashed his shot into the roof of the net from a tight angle.
The win has taken Hamburg to 13 points and fourth on the Bundesliga table, up from 10th, although the other teams have yet to play this weekend.
Augsburg remain 16th with just six points.