OK, I have done some extensive research on this and the candidates that I have found for the best QB/RB combination drafted by the same team in the same year are as follows:

1957 Cleveland Browns: Milt Plum and Jim Brown

2008 Baltimore Ravens: Joe Flacco and Ray Rice

1981 St. Louis Cardinals took: Neil Lomax and Stump Mitchell

1969 Buffalo Bills took James Harris and OJ Simpson

1949 Chicago Bears took George Blanda and George Taliaferro

1975 Chicago Bears took Bob Avellini and Walter Payton

1977 Dallas Cowboys took Steve DeBerg and Tony Dorsett

1980 Detroit Lions took Eric Hipple and Billy Sims

1989 Detroit Lions took Rodney Peete and Barry Sanders

1983 New England Patriots took Tony Eason and Craig James

1968 Oakland Raiders took Ken Stabler and Marv Hubbard

1987 Oakland(LA?) Raiders took Steve Beurlein and Bo Jackson

1990 Pittsburgh Steelers took Neil O'Donnell and Barry Foster

1961 San Diego Chargers took Charley Johnson and Billy Kilmer and Keith Lincoln

(this was when AFL and NFL were drafting same players. I believe neither Johnson nor Kilmer signed with Chargers...but went with NFL option. Lincoln did sign with Chargers)

2004 San Diego Chargers took Eli Manning and Michael Turner

2005 San Francisco 49ers took Alex Smith and Frank Gore

1973 LA Rams took Ron Jaworski and Cullen Bryant

1977 LA Rams took Vince Ferragamo and Wendell Tyler

But.....the best duo will undoubtedly be this combination:

2001 San Diego Chargers in the first round took LaDanian Tomlinson, and in the second round drafted Drew Brees.

As can be seen, though players may have been drafted together, that doesn't mean they stay together, like Brees and LT.