But the visitors were pegged back on the half-hour mark when Dale were awarded two penalties in quick succession. First, Michael Rose was brought down by Sam Morsy but George Donnelly's spot-kick cannoned off the woodwork.
Yet when Rochdale worked the ball back into the box, goalkeeper Tommy Lee was adjudged to have fouled Scott Hogan, paving the way for Andrew Tutte to convert from the spot.
Hogan then fired Dale into the lead with a fine individual goal in the 51st minute before Roberts levelled things up when he raced on to Jimmy Ryan's throughball to lob Josh Lillis.
"It was a really good game, two very good teams having a real go, both looking like they could score with every attack and I think the draw was a fair result," Spireites boss Cook said.
"I thought the first goal was going to be crucial because Rochdale are a really good team and Keith Hill has recruited really well. He knows how to set his teams up and he's a really strong manager in that sense.
"No team is going to come here and play Rochdale off the pitch - it just won't happen. So once we went 1-0 up I thought we would go on and win the game if I'm honest. I thought we'd get more space, more gaps to pick them off. Obviously the penalties were a big turning point, but they are what they are.
"We know the quality of our players and even when a couple of free-kicks and shots flew out of the ground we stuck by them and Jimmy Ryan and Gary Roberts have combined in the end. Seven points from three games, it's a good solid start."