Liverpool's 4-1 defeat at Arsenal meant the Saints would have moved up to fifth place if they had won at Goodison Park.
Ronald Koeman's side enjoyed plenty of possession and chances but they were unable to find a way past Everton goalkeeper Tim Howard.
Jagielka's goal from a corner in the 16th minute ultimately proved decisive.
Saints need only three more points to match their best ever Premier League points tally of 56, achieved under Koeman's predecessor Mauricio Pochettino last May.
However, given their impressive campaign, anything other than a top-six finish would probably be viewed as a disappointment.
And Koeman's side will end the weekend in seventh spot if Tottenham avoid defeat at Burnley on Sunday.
Everton may have eased any relegation concerns as they made it three in a row for the first time this season, but below the surface there were indications of a need to improve on a mid-table finish.
The Toffees started with Arouna Kone up front in the absence of the injured Romelu Lukaku but worryingly questions about the long-term future of the Belgium striker, who made a £28m switch from Chelsealast summer, remain.
Toffees have stuck with it
Lukaku changed agents last week and his new representative said on Friday that his client should not have joined the Toffees last summer, and "will play for one of the world's best teams" in the near future.
Without the presence of Lukaku, Everton struggled for a focal point in attack and it was Southampton who had the better of the first-half chances, although they would find themselves behind at the break.
Howard made a superb save to deny Saints striker Graziano Pelle, who had scored in Italy's 1-1 draw with England during the week, after he had got on the end of Shane Long's cross.
Everton then took the lead against the run of play when a Leighton Baines corner dropped to Gareth Barry and he steered the ball back across goal for captain Jagielka to side-foot home from close range.
James Ward-Prowse then went close twice, first curling a free-kick just past the post, then striking a swerving shot which an off-balance Howard managed to beat away with one hand.
Southampton saw plenty of the ball in the second half but found an organised Everton defence much tougher to break down.
Ross Barkley, who recently claimed his best position is playing behind the main striker, was withdrawn with 20 minutes left after a quiet display and his replacement Steven Naismith's appeal for a penalty when he went down in the box was ignored by the officials.
The visitors looked jaded in the remainder of the contest as they struggled to muster a meaningful effort and Everton closed out the game to record only their fifth home league win of the season.
Everton manager Roberto Martinez:
"It was as pleasing performance as you are going to get. It was a mature, and we were strong defensively. I though it was a good tactical battle and for us to keep a clean sheet was good. It was full of character, guts and desire.
"At times we had to manage the game and defend really well. Tim Howard came up with two magnificent moments and that's what makes Tim special. But the overall with the team display we defended well.
"Also it's great to see the sort of display from Phil Jagielka, John Stones and Gareth Barry with the way they all connected. Phil's goal is a magnificent way to top his performance."
Southampton boss Ronald Koeman:
"The final result is very disappointing, but not with the performance of the team. We played well. We were unlucky with the goal against us. The second half it was more difficult to create.
"Everton were good defensively and it was difficult to score and create chances after the break. However, we deserved a better result because we played well, but it's always about scoring.
"They scored one and we didn't score. If we continue with this level we'll maybe finish in a good position. We had a lot of ball possession, created chances. We did everything. But it wasn't quite enough."
