It was Mauricio Pochettino's first game at the helm and the Saints' new manager would have been delighted with his side's first-half showing, with the Toffees clearly outplayed and second best.
Rickie Lambert wasted a number of golden opportunities for the hosts and Everton were fortunate not to find themselves a couple of goals down by the half-time whistle.
David Moyes roused his troops during the break, as his side spent more of the second period in the ascendency, although both teams had opportunities to seal the win.
Overall, it was an especially disappointing performance from the Toffees, who were far from their best.
Here are six Everton-related talking points to take from this fixture.
As poor as Everton were in the first half, somehow they kept themselves in the game and even had the better chances to take all three points after the break.
Victor Anichebe made a big impression from the bench, and it was his precise pass to Nikica Jelavić that presented the Toffees with their best chance in front of goal.
Sadly for the well-stocked away support, the Croatian fluffed his lines, badly hashing at the ball when it seemed easier to score.
Jelavić has been woefully out of form for long periods this season, and apart from that miss, he was largely anonymous.
After scoring his fifth league goal of the season in early November, he's now found the net just once in his last 12 league outings.
Throughout his year at Everton, he's always been viewed as an indispensable factor, especially considering the dearth of quality in attack early last season.
However, it seemed particularly poignant that the Croatian was hauled off moments after his miss, despite the fact his side were still seeking a goal.
With the returning Kevin Mirallas taking his place—and playing centrally—and Anichebe looking far more of a handful for defenders, it seems his position is now suddenly under threat.
A positive to take from this performance was undoubtedly the contribution of Tim Howard.
Having appeared short of his best for much of the season, the American was back in superb form tonight, thwarting Lambert with a number of classy reflex saves.
Without this, the Toffees could have easily been out of the contest by half-time and nobody did more to earn a result for Moyes' side than Howard.
After going 16 league games without a clean sheet, it's now back-to-back shut-outs for the American, with this one especially deserved.
It's frustrating that it comes just as the Toffees have misplaced their potency at the other end of the field.
One of the main reasons Everton were so off-form in this game was due to their criminally low pass completion.
In total, Moyes' side averaged just 70 percent throughout the game, their lowest of the season, eclipsing the 71 percent in a 10-man effort away at QPR.
This greatly contributed to the disjointed spectacle as numerous moves were slowed down or broken up via some overly sloppy link-up play.
Everton were wayward all over the pitch, but especially in the final third, where just 59 percent of passes found their man. Again the lowest return of the season.
The worst culprits for the Toffees were Steven Naismith (52 percent) and Phil Neville (64 percent), but most players fell way short of their average contribution.
Only Leighton Baines (83 percent) and Marouane Fellaini (80 percent) passed at a respectable 80 percent or above.
The Toffees' passing woes had a knock-on effect in the creative department, as Moyes' side only fathomed out a meagre seven chances in this match.
Only once this season—away at Manchester City—have Everton created less in front of goal, once again highlighting just how below-par this performance truly was.
A particularly confusing aspect was the fact that the personnel was almost identical to last week's game against Swansea, where 16 chances were made—the joint fifth best return of the season.
For whatever reason, this was a lethargic showing in several departments, and it's important Moyes finds an immediate remedy.
Another positive to take from the gloom was the return of Kevin Mirallas after a long absence through injury.
As mentioned, he emerged from the bench to take the place of a misfiring Nikica Jelavić and initially took up a central berth, before dropping off Anichebe in the latter stages.
The Belgian seemed understandably off the pace, but his return will provide a much needed boost for the Toffees, especially after this anaemic performance.
He offers pace, trickery and an unpredictable element which could prove vital over the second half of the season.
Next week's FA Cup away tie at Bolton seems a perfect opportunity to bring him up to speed before once again unleashing him on Premier League defences.
After the 0-0 with Swansea, there was a deliberate attempt to remain upbeat and philosophical in the post-match report, but it's far harder to cling on to the positives here.
Everton were as bad as they've been all season during the first half. Although they improved after the break, they faded again towards the end and seemed void of the quality needed to win.
What adds to the frustrations is the sense of a missed opportunity.
Tottenham and Arsenal both dropped points at the weekend, meaning this was a golden chance for the Toffees to re-establish themselves in the conversation for fourth.
Most Champions League contenders are experiencing an especially gruelling run of fixtures at present, while Everton still wait for away trips to five of the six teams around them.
For the top four to remain realistic, this is very much the time to pick up points.