Cook brought the Benin international back to east Lancashire this season before joining the Spireites in October.
And Boco fired low into the net from 15 yards in the 65th minute to secure an important win for Stanley, who had been struggling with one win in 11 games.
However Chesterfield were ruing missed chances in the first half as they hit the woodwork twice in the space of two minutes.
Marc Richards, with his back to goal, hooked a shot onto the top of the crossbar and Mark Randall tried his luck from 45 yards was denied with Cameron Belford beaten in the Reds goal.
Sam Togwell was also one-on-one with Belford but the Bury loanee did well to keep him out.
Jack Lester enjoyed a pair of decent chances for the visitors but it was far from one-way traffic as Boco tested Chesterfield goalkeeper Tommy Lee and Padraig Amond had a header cleared off the line by Liam Cooper.
George Miller also came close for Accrington just before the break, stretching onto a Lee Molyneux cross but he could only steer the ball wide.
The Spireites were lively after the break, Belford pulling off a superb save to keep out a Lester close-range effort, but Boco collected Amond's pass on the left of the area and fired beyond Lee for his ninth goal
of the season.
It was then the Belford show as he was superb in preserving the lead, tipping over a Richards free kick and denying Tendayi Darikwa from close range. Sam Hird had a header ruled out for off-side for the visitors in the final minute as Stanley held on.
