Walker had tied a course record with a 62 Saturday, good for a fourth-place tie. But he remained steady as overnight leader Brooks Koepka stumbled, emerging with his first win in his 188th PGA start.
He finished the tournament at 17-under-par 267, two shots ahead of Vijay Singh, who carded a 3-under 68 for his best tour finish since taking second at the 2011 Northern Trust Open.
Sharing seventh place one shot further back were George McNeill (71) and Brian Harman (65).
Will MacKenzie (69), Billy Hurley III (68) and Max Homa (69) each held of share of ninth place at 12-under 272.