Cheltenham stunned Colin Calderwood’s men by taking a 20th-minute lead when Steve Gillespie raced clear of the Forest defence and beat Paul Smith.
But Forest came storming back and six minutes later Agogo brilliantly controlled a cross from Sammy Clingan and found the back of the net.
Seconds before half-time Luke Chambers nosed the home side in front when he scored his eighth goal of the season after a header by Garath McCleary had come back off the bar.
And Forest made sure of the points two minutes after the break when Agogo cut inside and scored from outside the box. Cheltenham twice hit the bar with headers by Gillespie and Ashley Vincent but they were nevertheless a well-beaten side.