As so often this season top scorer Reid was the home side's hero.
Reid fired the hosts ahead in the 28th minute, sending an angled drive from the right past diving goalkeeper Tommy Lee and in off the far post.
Chesterfield responded with Ritchie Humphreys' 57th-minute strike from the left side of the area that deflected off Argyle midfielder Andres Gurrieri to send it past home keeper Jake Cole.
Reid restored Argyle's lead with a brilliant solo goal two minutes later, skipping between four defenders on the edge of the penalty area before rifling a 20-yard rising shot into the net.
Sheridan said: "Reuben was a threat. He could have probably had a hat-trick. But I don't want to single out just one player because we are all in this together and the team won us the match.
"It was a great result and great performance as well. I think we had a desire and work ethic just to get the three points we were after.
"I thought we were brilliant, we battled when we had to battle but created some good chances as well. We should have scored more goals, we were always lively on the break with pace a nd when we had to defend, we defended.
``There were one or two crosses that flew across our box but we have created plenty of opportunities and I thought we were well deserved winners.
"I thought we looked a fit team again, we never say die and we kept going until the end and we have done that a few times this season.
"I was disappointed that they equalised. We were playing too deep at the start of the second half.
"After Reuben scored a brilliant second we pushed up 10 or 15 yards and I think it helped us hell of a lot."
Chesterfield arrived at Home Park as league leaders but finished the night in second spot and a point behind new table-toppers Rochdale, who won 3-0 at Northampton.
Spireites boss Paul Cook said: "All we talk about at this stage of the season is results. It doesn't matter whether you play well, we have been beaten 2-1 and have got a long trip back to Derbyshire.
"But we have got to pick ourselves quickly up because we have got a massive game both for ourselves and our supporters at Mansfield on Saturday.
"We have said all the way along there are bumps and bruises but it's a promotion campaign we are on. It doesn't mean that you finish in a promotion place or a play-off place it means you need to finish the season as strongly as possible.
"Tonight we are very disappointed because we felt in the second half that we were never going to lose the game and we were in the ascendancy.
``It was a question of if we could score, when we could score and when we'd get the next one. You know we never felt under any pressure but you have got to take your hat off to Plymouth because they won."
- Sports & Recreation