Skipper Lee Collins and Alex Bray were too unwell to play and Rovers goalscorer Reuben Reid was one of those who had missed training during the week.
“Reuben has been really poorly and got off his sick bed today,” Cooper said. “He got through an enormous amount of work and capped it off with a goal.
“A lot of players were suffering with illness and it was a case of just getting the three points and I thought we came to life in the second-half and moved the ball quickly and deserved to win the game.
“We needed to get to January to strengthen and that is what we have done, but we have to kick-on now and get some results on the road.
“We gave away a cheap free-kick and if you do that you run the risk of somebody bending one in and I thought we should have avoided that, but once their guy got sent off it was about exploiting the gaps and getting Dayle Grubb and Dan Wishart on the ball and I thought we did that in the second half.”
Luke Wilkinson gave Stevenage the lead with a well-struck free-kick in the 26th minute but the visitors were reduced to 10 men after half an hour when Alex Revell was sent off for his challenge on Isaiah Osbourne.
Reid levelled the scores in first half injury time before Rovers took charge of the second half with Grubb having an effort cleared off the line.
Farrend Rowson headed the home side into a 61st minute lead and Christian Doidge rounded things off with a close-range effort after good work out wide by Osbourne.
Stevenage manager Darren Sarll was disappointed by Revell’s red card and the performance of referee Graham Salisbury.
“It seems that every game we play we’re playing against the four men in black,” he said. “They always let you down and I don’t think it’s fair on supporters. I thought he (Salisbury) got loads wrong for us and it’s scary.
“For the Revell sending off, he’s kicked the ball first and is the other lad not late? He kicks the ball so then any other contact after that must be the other player being late.
“You have to go chasing it at the end – at 2-1 you’ve lost your three points so you might as well lose by two goals than one. There was a little 10 minute period when Luke Amos got control of the game and passed it around which you have to do when you’ve got 10 men.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.