Valencia hadn't scored a club goal since netting twice for West Ham against Manchester City in January 2016.
But the 27-year-old was back on the scoresheet at Goodison Park as he bagged his first goal in 12 appearances since joining on loan from West Ham.
Valencia's second-half strike was followed by late goals from Leighton Baines and Romelu Lukaku, ensuring Everton manager Ronald Koeman could savour a winning start to 2017 at the expense of his former club.
After Everton lost 1-0 on Koeman's first return to St Mary's earlier this season, the Dutch coach condemned Southampton to a third successive defeat that represented their worst losing run in the league for more than two years.
It took Southampton just 41 seconds to score when they faced Everton in November, but the early stages weren't so kind to them this time.
In the third minute, Saints right-back Cedric Soares was forced off in the third minute after sustaining a nasty gash in his head following a collision with an advertising board around the pitch.
Everton midfielder Ross Barkley threatened to add to Southampton's problems with a powerful strike that was pushed away by Fraser Forster.
Koeman had given a first start to 19-year-old forward Dominic Calvert-Lewin, but his chance to impress was curtailed by an early injury after just 11 minutes.
Jay Rodriguez went close twice in quick succession with a snap-shot pushed away by Everton goalkeeper Joel Robles and then a powerful effort over the bar.
With both sides struggling to find any momentum after the interval, chances were at a premium and even when Nathan Redmond was clean through he fired straight at Robles after a rare menacing moment from Southampton.
But Valencia had come on for Aaron Lennon after 61 minutes and the Everton substitute broke the deadlock 12 minutes later with a close-range finish after Lukaku's header had been parried into his path by Forster.
Everton's second goal owed much to the threat posed by Valencia as he forced a rash challenge from Saints defender Maya Yoshida in the 81st minute, earning a penalty that Baines dispatched with typical efficiency.
Lukaku sealed Everton's late goal blitz in the 89th minute when the Belgium striker took a Tom Davies pass and blasted into the top corner.