We characterize the voltage-driven motion and the free motion of single-stranded DNA (ssDNA) molecules captured inside the approximately 1.5-nm alpha-hemolysin pore, and show that the DNA-channel interactions depend strongly on the orientation of the ssDNA molecules with respect to the pore. Remarkably, the voltage-free diffusion of the 3'-threaded DNA (in the trans to cis direction) is two times slower than the corresponding 5'-threaded DNA having the same poly(dA) sequence. Moreover, the ion currents flowing through the blocked pore with either a 3'-threaded DNA or 5' DNA differ by approximately 30%. All-atom molecular dynamics simulations of our system reveal a microscopic mechanism for the asymmetric behavior. In a confining pore, the ssDNA straightens and its bases tilt toward the 5' end, assuming an asymmetric conformation. As a result, the bases of a 5'-threaded DNA experience larger effective friction and forced reorientation that favors co-passing of ions. Our results imply that the translocation process through a narrow pore is more complicated than previously believed and involves base tilting and stretching of ssDNA molecules inside the confining pore.