Walker almost doubled his tally shortly after with a header from six yards but it was saved by keeper Danny Alcock.
Tamworth failed to rally after the goal and also had Bradley Pritchard sent off for a professional foul late on.
Barrow: Deasy, Spender, Jelleyman, Jones, Bolland, Hulbert, Rutherford (Logan 34), Boyd, Walker, Shaw, Foley (Bond 83).Subs Not Used: Tomlinson, Pearson, Dugdale. Booked: Hulbert, Jones, Walker. Goals: Walker 77 pen.
Tamworth: Alcock, Tait, Briscoe, Blackwood, Smith, Rodman, Wright, Sheridan (Benjamin 84), MacKenzie (Hurren 81), Shaw, Pritchard.Subs Not Used: Nicholson, Lyttle, Lake-Gaskin. Sent Off: Pritchard (90). Booked: Shaw.
Att: 1,051. Ref: D Handley (N Yorkshire).
Source: BBC Sport
Source: BBC Sport