A goal in the fifth minute by recalled striker Marc Richards brought them a second successive win, and breathed new life into their faint hopes of making the play-offs.
But it needed a hard-working and determined second-half showing to earn the victory against an Oxford side that had won its previous two matches, and which dominated the first half after falling behind.
Cook said: "I thought we were in complete control in the second half. We offered Oxford very few attempts on goal, and I thought we might have nicked a second goal on the break. After initially starting well, and scoring, we sat back in the first half which invited pressure onto us.
"We weren't happy about that, so we had some good words with the players at half-time. I wasn't going mad at them, I just thought we needed to take the game to Oxford much more, and in the second half we did that, and it paid off.
"All of a sudden we're not conceding many goals, and we're winning matches."
For Cook, it was a contrast to his previous visit to the Kassam Stadium this season when he was boss of Accrington, and left licking his wounds after a 5-0 thrashing.
And he said he was delighted for Richards, who bagged his seventh goal of the season, with a well-taken strike across keeper Luke McCormick and into the bottom corner, from Richard Brindley's pass.
Cook said: "I'm made up for Marc. He never got in the Chesterfield line-up last week, today he did, he scored, we kept a clean sheet and we won.
"In the second half we played very well. It's a happy day, but I know that in football next week might not be so happy."