Davis finished off a crisp passing move on the half-hour mark to open the scoring, before Pelle headed home a second minutes later to double the advantage.
The Cherries improved after the break and were thrown a lifeline when Victor Wanyama was sent off on 78 minutes, but the Saints held on.
Below, relive the drama with our live text commentary.
Let's not beat around the bush - Saturday's Premier League action was good, but it wasn't great. In Trick or Treat terms, there was a lot of monkey nuts, bananas and Bounty bars smuggled into our black sack of goodies by clever parents - or managers, in this ill-conceived analogy - who knew we wouldn't notice until it was too late. We're looking at you Van Gaal. But week 11 isn't over yet. Nope. Today at St Mary's, Southampton and Bournemouth will make it rain with Skittles and fun-size Mars bars in an effort to atone for some low-key affairs yesterday. Both sides will produce the fireworks that illuminated skylines around the world last night and we've got every minute of it to come. Or it'll be a 0-0. Who knows.
Like the contents of your children's calorie-laden candy sacks this morning, there's still quite a bit to chew on this afternoon. First, though, we'll look at team news. Actually, first you good people can watch what the fellas down at Sports Mole HQ have had to say on this one. Then we'll dig up some team news.
Right, let's start with our hosts and Mr Ronald Koeman is unchanged from last week's 1-1 draw at Liverpool - we mean his team, not his clothes. Graziano Pelle spearheads the attack, with Sadio Mane in behind him causing havoc as per usual. Shane Long is still out injured with an ankle problem so Spaniard Juanmi is the only goalscoring option for the Saints on the bench.
On to the Cherries now and Eddie Howe - who, if we're honest, looks young enough to get away with trick or treating - makes three changes from the 5-1 defeat by Tottenham last time out. The injured Artur Boruc misses the trip to his former club as Adam Federici starts between the sticks. Defender Adam Smith comes in for Steve Cook, while Harry Arter is finally given a Premier League debut as he replaces Joshua King to start in a five-man midfield, behind Glenn Murray up top.
Interestingly, this one is a local derby. Okay so it might not have the verve of, say, Arsenal - Spurs, and one fan isn't going to take the hurt of a defeat out on a horse like, say, a Newcastle supporter might after losing to Sunderland, but it's a derby nonetheless. Thirty-one miles separate both clubs, but this is only the second time that both sides have shared the same division for, hmm, 55 years!
Consequently, our head-to-head segment will be a little light. Actually, as far as head-to-heads go it'll be like comparing the Headless Horseman to Gwyneth Paltrow in Se7en. There is something to work with, though, and I can confirm that Saints won the last two meetings, when both sides were in League One four years ago. Southampton are bring a four-match unbeaten streak against Bournemouth. In fact, their last defeat to the Cherries was when they were known as Bournemouth and Boscombe!
Southampton endured a lukewarm start to the campaign, following on from a hugely encouraging 2014-15 season. Koeman's men picked up two points from a possible nine early doors, before a 3-0 win over Norwich City saw them get off the mark. A false dawn? Yep. The Saints drew with West Brom, before losing 3-2 at home to Manchester United and they were back to square one.
Things have looked markedly brighter in recent weeks, however. They beat Swansea City and Chelsea 3-1 in back-to-back victories, and drew 1-1 at Liverpool, under Jurgen Klopp, last weekend. In truth, they could have beaten the Reds on another day following an excellent first-half display, but Sadio Mane's late equaliser saw them steal a point.
On to Bournemouth now and the Cherries, in their maiden top-flight season, have won twice - away to West Ham and home to Sunderland. The good news is that a third win here would lift them four points clear of the relegation zone. The bad news is that they haven't won a game since Callum Wilson - who had five goals in six Premier League games - was ruled out for the season.
There's big, big pressure on Glenn Murray for them this season. He's done alright since securing a deadline-day move from Crystal Palace, scoring twice in his last three games, but is he going to get the goals to keep Bournemouth in the Premier League? That's the £40m question, my friends.
PREDICTION! Twenty minutes to go - let's get a prediction wrong. Given that Bournemouth have shipped 10 goals in their last two league outings, this one seems like a game in which Sadio Mane, in particular, could wreak havoc. 3-0 Southampton, with Mane scoring twice. Pelle with the other. This is the part where Bournemouth win 1-0.
Just need one goal in the first half of the Southampton/Bournemouth game to finish an acca and a top day of betting
— Fourth Official (@FourthOfficial_) November 1, 2015
Plenty of noise from both sets of supporters early on, which is nice because very little has opened on the field. Saints have plenty of possession but they've done little at the final third as of yet.
Mane gives Adam Smith a glimpse of what he's up against this afternoon with a bit of trickery down the left-hand side, but the Cherries defender does well to be fair. That certainly seems like an avenue of attack this afternoon for the Saints.
Southampton get in behind Bournemouth for the first time as Davis threads through Pelle, who has the angle against him but he goes for goal anyway and it's deflected wide by Simon Francis. The corner comes to nothing.
Bertrand does excellently to reach Van Dijk's searching ball here, but it just goes out of play after the ex-Chelsea man fizzed it into the box. Southampton well on top in this first 10 minutes.
CHANCE! We said Mane was a huge threat today, and he almost opens the scoring. Pelle, who collected Soares's low cross, pokes it into the path of Mane, whose first-time effort just inside the box is narrowly over following a block from Distin. The corner comes to nothing.
CHANCE! Saints wreaking havoc. Bournemouth can't get out of their own half, and Pelle nods a long ball down to Mane again but the Senegalese winger drills a half-volley over the bar. This can't possibly be 0-0.
A loose pass from Surman is pounced on by the omnipresent Mane, who spreads the ball wide to the overlapping right-back Soares, but he gets caught in two minds and the counter breaks down. Bournemouth are certainly on the back foot.
'There's only one Harry Redknapp' echoes around St Mary's now and there's no prizes for guessing which fans are chanting it. That's been the best thing that has happened in the last few minutes unfortunately.
Every Southampton fan, and most of the hosts' players, wants a penalty now after Jordy Clasie's volley cannoned off Francis, but it was his chest and not his hand. Saints well on top. Bournemouth have been rather disappointing.
Southampton have had 84% of the ball for the last 10 minutes, which just about sums it up, but Bournemouth working exceptionally hard off the ball to their credit.
Well, it's been coming and this is a brilliant, brilliant opener for Southampton. Jordy Clasie plays it to Pelle, whose beautiful first-time layoff releases Tadic down the left. The Serbian then drives a wonderful cross into the box for Davis, who pulled away from Distin, and the Northern Irishman volleys home. Fine goal.
We predicted 3-0 and they've already got two. The big Italian shrugs off the massive Distin to nod home another wonderful cross from Dusan Tadic. Bournemouth have been abysmal.
Worryingly, Bournemouth have no response whatsoever and Southampton could quite easily nick a third before half time. The Cherries are fit for the bonfire.
Three minutes to go until the break and Bournemouth don't look like doing much. They've got injuries, fair enough, but this is still really, really disappointing.
Southampton totally, totally in control and goals from Davis and Pelle have earned them a 2-0 half-time lead. The visitors have done very, very little and, in truth, they deserve the hiding they're on to here if we're honest.
Bournemouth, to their credit, do look a little better since the couple of half-time subs, but they're still two goals down. Problem is, can they stop Southampton from scoring again and, well, I doubt it.
Bournemouth are certainly having a go but they're losing possession in their counter-attacks far too easily. Credit to Howe for changing it, but as we mentioned, it's still a huge ask and, despite their possession and momentum, no chances are being created.
Craig Pawson is doing Southampton quite a few favours here. Pelle just fouled Arter but nothing doing. Minutes previous, Wanyama bundled over Smith but nothing doing.
Oh lord. Adam Smith has been really poor this evening and another counter-attack breaks down when his cross flies over the head of everybody. Unperturbed, Bournemouth are carrying on in the same vein. They've won me over in this first 15 minutes or so.
Good defending from Charlie Daniels here as he wins the ball from Sadio Mane. Southampton are penned here, my friends. Bournemouth fans want a handball against Maya Yoshida now, but it was his chest.
SUB: Right, twenty minutes to go and Ward-Prowse replaces Jordy Clasie now. I'll put myself out there - I don't see Bournemouth scoring. This is excellent defending from the hosts.
SHOT! Wanyama drills well, well wide, but that's better from Southampton, who have been tonked in this second half in terms of possession. They've only had 24% of the ball!
Fifteen minutes to go at St Mary's and the visitors continue to toil in Southampton's half, but the hosts have been well drilled defensively. They all know their jobs.
RED CARD FOR WANYAMA! Stupid from the Kenyan, who slides in and brings down Lee Tomlin, having already been booked. So poor. Bournemouth have a free kick in a dangerous spot now.
The first corner comes to nothing, and so does the second as Gosling heads over. Bournemouth have been given the slimmest of lifelines here, but Southampton have probably done enough. Still, about nine minutes of normal time to go.
SHOT! Matt Ritchie drills over the bar from outside the box. That's honestly as close as they've come - and it wasn't even close. Despite their possession, and momentum, they haven't tested Stekelenburg once.
Bournemouth had possession and momentum in the second half, but Southampton's first-half goals through Davis and Pelle were enough to clinch all three points. Wanyama's red card 12 minutes from time threw the Cherries a lifeline, but the hosts defended brilliantly it has to be said, limiting the visitors to no real chances to speak of. Anywho, that's us. Cheers for tuning in and we'll see you next time.
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