Warrington looked set to complete an amazing fightback until Jones-Bishop got the ball down from Max Jowitt’s kick with two minutes left.
It was Wildcats’ eighth win out of nine competitive games since Chris Chester took over as coach before Easter.
Wakefield led 12-0 after seven minutes, 24-6 at the break and were 24 points clear just four minutes into the second half, but Warrington showed champion qualities by battling back.
Max Jowitt’s offload created the opening for Craig Hall to score the first try, then the impressive Matty Ashurst crossed from Jacob Miller’s smart pass.
Joe Westerman pulled a try back for the visitors, Kurt Gidley converting, but Hall intercepted Ben Westwood’s pass to go over for his second and then he did the same to Gidley to set up a try for Tom Johnstone.
Liam converted all four and booted a fifth goal at the start of the second half after Miller had put Ashurst in again.
That made it 30-6, but Warrington sparked into life with three tries in six minutes, through Daryl Clark, Gidley and Matty Russell, Gidley converting two of them.
Russell’s try came when Wakefield were down to 12 players, with Jones-Bishop in the sin-bin for a professional foul.
He had tackled Jordan Cox, who made a huge break from the re-start, but took too long to get off.
Finn booted a penalty goal, but then Anthony England and Gidley were yellow-carded for fighting with 11 minutes left.
The penalty went to Warrington and from it Smith put Westerman in and then cut the gap to four points with his conversion.
Four minutes from time Wakefield were down to 11 men when captain Danny Kirmond was yellow-carded for tripping Smith, but Jones-Bishop made a try-saving tackle on Kevin Penny and then touched down at the other end to seal an outstanding win for the hosts.