It seemed Danny Wilson's side would escape the City Ground with a share of the spoils after Richie Barker headed the visitors level in the 38th minute.
Kris Commons had initially put the home side ahead with a neatly-taken goal in the 11th minute.
But Forest had failed to make the most of their domination - until Agogo popped up seven minutes from time to secure their fourth win in five matches.
Commons had been restored to the starting line-up after scoring twice in two substitute appearances - and it took him only 11 minutes to make his mark against Hartlepool.
Julian Bennett crossed from deep into the danger zone, where Agogo's neat header down provided the in-form forward with a simple finish from close range.
It was a flying start by Forest's standards, with Calderwood's side having failed to score prior to the 43rd minute in their previous three matches, despite long periods of supremacy.
That was to be a factor for Forest again here, however, as they saw a combination of poor finishing and fine goalkeeping from Jan Budtz hold them at bay as they went in search of a second.
Chris Cohen and Agogo both came close to scoring - before hard-working Hartlepool drew themselves level on the break.
Former Forest man Ian Moore was the catalyst, as he crossed dangerously into the box where Barker stooped to head beyond Paul Smith and into the back of the net.
It could have been worse for the home side, as they saw Hartlepool spurn a golden opportunity to snatch the lead, after defender Kelvin Wilson lost his footing and left Gary Liddle with only Smith to beat - with the keeper making a fine save with his feet.
But they too could have regained the lead in first-half stoppage time, as Agogo latched onto a Nathan Tyson flick, only to see Budtz save yet again.
Forest came close again as a whipped-in ball from Sammy Clingan eluded both Tyson and Agogo on the edge of the six-yard box - with Tyson injuring himself as he threw himself at the ball and having to be replaced by Grant Holt.
But Smith also had to produce a fine save at the other end, as Moore rifled in a low shot that the keeper did well to palm around the post.
Forest finally made the breakthrough in the 83rd minute however, as Budtz made a superb save to deny Commons, but could do little as Agogo lashed home the rebound at the near post.