After two games with out a win there was an edgy feel to the Priestfield but goals from Antonio German and Chris Whelpdale proved the difference as Plymouth dropped to the bottom of the Football League.
Jason Banton pulled one back for the visitors but it was nothing more than a consolation goal and, with Port Vale surprise losers at home to Southend, Gillingham extended their lead at the top of the table.
"It was the best performance for a while. At this time of year, anxiety and tension are high and it's difficult to win at home," said Allen.
"That's not just at Gillingham, it's the same in the division above and the division above that. But as a manager you can either hide behind it or do something positive about it.
"But we thought we would create an action plan and the players deserve all the credit because they went over the white line and they put in a performance.
"It was good to watch, it was nice to see our team play with a lot more confidence and belief in front of our home supporters.
"We played great football, we knocked it about, we moved it around the pitch, we were tenacious and hungry. It took a lot of courage.
"The players put in the performance and the supporters enjoyed it. Our supporters are full of passion and it was nice of us to give something back. They will probably have to get health and safety in because the noise levels in here were quite incredible."