Liverpool regained their advantage in the 79th minute as Daniel Sturridge converted Sterling's header from close range, but had Mignolet and the woodwork to thank for holding onto the lead as the keeper tipped Morgan Schneiderlin's powerful effort onto the bar in the closing stages.
Here, Sports Mole takes an in-depth look at an entertaining 90 minutes on Merseyside.
On target: 5
On target: 6
Was the result fair?
Statistics can often give a misleading view of a match, but on this occasion they are a fairly accurate representation of the game. It was an even encounter, with both sides enjoying spells in the ascendency over the 90 minutes. Southampton struggled to get into the match at first, but really improved as time went by and deserved a point this afternoon.
The Saints certainly had the chances to draw, or even win the match, with Steven Davis, Schneiderlin and Shane Long all missing gilt-edged opportunities. Liverpool, on the other hand, were more clinical and made the most of their best openings.
That ultimately proved to be the difference this afternoon as Liverpool rather clung on to the slender lead. The hosts will feel fortunate to have come away with all three points, while Southampton will feel that they deserved something from the game.
The Reds were certainly not at their free-flowing best this afternoon, but they showed signs of what made them so dangerous last season. Sterling's pace was a constant threat, but the likes of Philippe Coutinho, Sturridge and Steven Gerrard struggled to have much of an impact.
A lot of credit has to go to Southampton for that, but it is also partly down to the fact that teams no longer have to worry about Suarez. They can instead focus their attention on the other players, stunting their influence on the game.
Even so, Liverpool did enough to grind out a victory today, and Brendan Rodgers will be delighted at having come away with three points. It was by no means as comfortable as many people were expecting, and improvement is certainly needed on Liverpool's part, but to start the season with a win is exactly what the Reds would have wanted.
Despite the obvious disappointment at the result, Southampton fans must be happy with what they saw this afternoon. After a summer of woe that saw them lose their manager and a number of their most important players, forecasts were grim for how the Saints would fare this season.
However, they looked every bit the match of Liverpool for large periods of the game and deserved at least a point from Anfield today. Their failure to draw the game is partly down to poor finishing, good goalkeeping and a bit of bad luck, but there are plenty of positives for new manager Ronald Koeman to take.
There were pre-season predictions that Southampton could be embroiled in a relegation battle this season, but if they play like they did today over the next 37 matches then they will be a top-half team once again. The defeat will be hard to take, but things are looking a lot brighter for the Saints now than they did before kickoff.
Sports Mole's man of the match
Raheem Sterling: Suarez's name is likely to come up a lot when talking about Liverpool this season, not least because they need players to step up and fill the void left by the new Barcelona striker. Sterling is at the forefront of that, and he got off to a fine start this afternoon.
While the likes of Coutinho and Sturridge struggled to shake off Southampton's defence for long periods, Sterling always looked a threat with his pace and trickery. His first goal was very well taken, and he showed another side to his game by winning the header that led to the deciding goal.
This one goes to Steven Davis for a glaring miss when the scores were locked at 1-1. Just seven minutes after the Saints had equalised, James Ward-Prowse slipped the ball to Davis, who had time and space to pick his spot from inside the box. However, he sent a weak effort towards the bottom corner which was fairly comfortably saved by Mignolet.
Long also deserves a mention for his miss following Schneiderlin's effort off the bar, with the ball bouncing down to the debutant, who nodded wide from close range. That wasn't quite as bad, however, as he was under heavy pressure and seemed to see the ball late.
Mark Clattenburg had a fairly quiet game this afternoon. He had one or two minor penalty shouts which he correctly turned down, and only had to produce three cards.
Liverpool: Next up for last season's runners-up is a match against the reigning champions. Liverpool take on Manchester City at the Etihad Stadium next Monday.
Southampton: The Saints, meanwhile, host West Bromwich Albion at St Mary's on Saturday.