Downing put the Saddlers ahead in the 14th minute, but deflected a long-range shot from O's skipper Nathan Clarke, which was going wide, past his goalkeeper Richard O'Donnell in the 77th minute, which condemned Walsall to a 10th game without a win.
Walsall began brightly and in the sixth minute Orient goalkeeper Eldin Jakupovic did well to turn a shot from Milan Lalkovic on to the post before the ball was scrambled clear.
But the Saddlers were rewarded for their early pressure when they took the lead in the 14th minute as Craig Westcarr's corner, struck low into the goalmouth, reached the recalled Downing, who drilled the ball into the back of the net.
Orient eventually started to ping the ball around sweetly and the home defence had several close shaves.
Moses Oduajo whipped over a cross which no-one could quite reach, then David Mooney's drive was deflected into the hands of O'Donnell in the 26th minute.
Orient were much the better side in the second half, but O'Donnell kept out drives from Chris Dagnall and Mooney before Downing's own goal hauled them level, while Mooney headed straight at the goalkeeper twice in stoppage time.