With four players allowed to represent each team over the course of a round, the final was staged over two singles and one doubles match.
Parker won his singles tie 6-4, 6-2 over Menorca’s Oscar Mesquida-Berg, before Oscar’s brother Alex Mesquida-Berg levelled the scores with a 6-3, 6-1 win over Watkins.
That meant that the fight for the gold medal went down to the doubles match, with the same duos as in the singles.
Jersey won the first set 7-6 on a tie break but Menorca levelled winning the next set 7-5. At one set all, the final set went immediately to a tie-break format with Jersey prevailing 10-8 in a gripping finale.
Parker said of victory: “It was one of our goals when we came here to win team gold.
“To do it the way we did, after losing out on four or five match points, then saving the match point, makes it a little bit better.”
Watkins added: “For me it’s probably a little bit different.
“Stuart is going for three golds here so I felt a bit of pressure to get the team done early on.
“We had loads of chances and we probably should have closed it out earlier than we did.
“But to hit a let cord at 9-8 down to save match point, after that we probably knew it was going to be our day.”
Both players appeared to share a good relationship on the court, and were supported throughout by team mates and staff.
Parker said of the support: “Our whole team should get praise, it’s not just me and Mike who have won it.
“Jeremy (Cross) on Court 4 practices so many hours and Jack (Hodges) is the main supporter – he’s new to the team so this is his first Games.
“Andrew (the coach) helped us out in the doubles, and Wayne (manager) who is also Stuart’s dad.
“It was a real team effort.”
Parker competes this morning in the men’s singles, against David Thomas of Bermuda.
Parker and Watkins received a bye from the round of 32 in the men’s doubles.
In the women’s team final, Gibraltar won their first gold medal of the Games.
Amanda Carreras won her singles match 6-0, 6-0 over Isle of Man’s Laura Feely.
In the second singles tie, Lindsey De Haro-Sene was defeated 6-3, 6-1 by Katie Harris.
The two Gibraltarians combined in the doubles match to defeat Feely and Karen Faragher 6-4, 6-2.