The 24-year-old beat GB team-mate Alfie Hewett 6-2 6-1 in 54 minutes to collect his second medal in Rio.
On Thursday, Reid and Hewett had to settle for silver in the doubles event, losing out to French pair Stephane Houdet and Nicolas Peifer.
Reid won the inaugural singles title at Wimbledon this year as well as the Australian Open title.
"I felt I hadn't played that well on the big stage until Australia this year and ever since then I've enjoyed every match on the big stage," said Reid after his latest triumph.
"I was nice and relaxed and managed to play one of the best matches of my life.
"Me and Alfie know each other inside out. We train together, we play doubles together. It just felt like anything I tried tonight came off.
"It's an incredible feeling. I'm really clear headed at the moment but I might just lose the plot as soon as I get back to the locker room."

Gerard Coyne, who is challenging Len McCluskey for the leadership of Unite, said his rival was "seeing plots all over the place".
He said Unite should not be focusing on "the extreme politics of the left".
Mr McCluskey claims a "cabal" of MPs are treating the leadership contest as a "proxy war" against Mr Corbyn.
But speaking on BBC Radio 4's Today programme, Mr Coyne, the union's West Midlands secretary, said: "Len is seeing plots all over the place and actually it is only him that has lost the plot in this election.
"He is rattled, he can see it slipping away from him, and he is lashing out with allegations about involvement in this campaign."
The battle for control of Unite, Labour's biggest donor, has become increasingly bitter, with insults and accusations traded between Mr McCluskey and Mr Coyne.
Fujitsu rep Ian Allinson completes the three-way line-up, and voting ends on 19 April.
Mr McCluskey is a key ally of Mr Corbyn, and has suggested the Labour leader should be given 15 months to turn around his party's performance in the polls.
Mr Coyne said he would offer no such "shelf life", but added that he had not supported Mr Corbyn's bid for the leadership, saying: "I would prefer the Labour Party to be able to form the next government."
On Sunday Mr McCluskey told the Observer Mr Coyne's campaign was being "run by a cabal of West Midlands MPs who are trying to abuse Unite's democracy by fighting a proxy war against Corbyn".
He has also labelled his rival a "puppet" for the media and the "right wing of the Labour Party".
Mr Allinson, who calls himself the "grassroots socialist" candidate, said the resources being spent on Mr McCluskey and Mr Coyne's campaigns should instead be spent on fighting for Unite members' jobs.
Scotland's Gordon Reid won Paralympics gold in the wheelchair tennis singles final.
[NEXT_CONCEPT]
The man hoping to unseat the leader of the UK's largest trade union has dismissed claims he is part of a plot to undermine Jeremy Corbyn.