We present results for antilambda and antiproton production in Au+Au collisions at 11.7 A GeV/c including spectra and extracted invariant yields for both species in central and peripheral collisions in the rapidity range 1.0<y<1.4. The antilambda yield increases from dN(Lambda;)/dy = 1.2(+0.7+0.2)(-0.6-0.2)x10(-3) in peripheral collisions to 19(+4+3)(-5-2)x10(-3) in central collisions. The direct antiproton yield is deduced from the measured total antiproton spectra to extract the ratio of antilambda-to-direct-antiproton production. The Lambda/p ratio near midrapidity increases from 0.26(+0.19+0.5)(-0.15-0.4) in peripheral collisions to 3.6(+4.7+2.7)(-1.8-1.1) in central collisions, a value larger than current theoretical estimates.