Manager Claude Puel selected Rodriguez in place of the injured Charlie Austin (shoulder) for the trip to Bournemouth and was rewarded with an energetic performance that could herald the start of an extended run in the side.
"It is massive for me and for my family," Rodriguez told British media after scoring his second and third league goals of the season and his fourth in all competitions since September last year.
"They've been through it (the injuries) with me as well and to be part of the team... and grind out a win is a great feeling."
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Seventh-placed Southampton return to action against Tottenham Hotspur on Dec. 28 and Rodriguez is looking forward to the 10-day break between matches after a hectic schedule that has seen them play two games a week over the past month.
"We've had so many games," he added. "We have travelled a lot and it has been quite tough, especially as it is new for a lot of players, including myself.
"So it will be nice to have a small break from games, continue to work hard and get my head down and keep improving."
(Reporting by Hardik Vyas in Bengaluru)
