Although the scoreline suggests a tight match, the champions dominated throughout and could have won far more comfortably had Fraser Forster not performed as well in the visitors' goal, while Eden Hazard had a strike ruled out for a marginal offside against substitute Cesc Fabregas.
The win moves Chelsea level on points with second-placed Manchester United, who travel to West Brom on Sunday, while Southampton - who dropped Virgil van Dijk - are winless in five Premier League matches.
Chelsea were on top throughout the first half at Stamford Bridge, with Forster making multiple saves and a Pedro effort deflecting onto the post.
The impressive Alonso broke the deadlock just before half-time, though, bending a delightful free-kick into the bottom-left corner from 25 yards out for his fourth goal of the season.
Charlie Austin had two fine chances to level the scores but could not find a way past Chelsea goalkeeper Thibaut Courtois, whose saves secured a fourth successive Premier League victory over Southampton for the Blues.
Southampton rang the changes after a 4-1 loss at home to Leicester City last time out and they created the first opening at Stamford Bridge, Chelsea captain Gary Cahill clearing a dangerous low cross from former Blues full-back Ryan Bertrand at the second attempt.
Willian burst into the box in the 14th minute thanks to a sublime one-two with Alonso, but the Brazilian sliced a presentable opening wide of the upright.
Forster punched away an Alonso volley and the goalkeeper then made saves from Cahill and N'Golo Kante shot as Chelsea cranked up pressure.
Terrific wing play from Willian created another opening for Alonso after 32 minutes, but Forster got down quickly to push the Spaniard's arrowed strike around his right-hand post.
Chelsea continued to exploit weakness down Southampton's right after Cedric Soares' 17th-minute exit due to injury, Pedro cutting inside but seeing his shot deflect onto the woodwork.
And on the stroke of half-time, Chelsea scored the goal their dominance deserved. Hazard's driving run was ended by Maya Yoshida, with Alonso stepping up to beat Forster with a dipping effort from the resultant free-kick.
7 - Chelsea have scored seven direct free-kicks under Antonio Conte in all competitions, more than any other Premier League side since the start of last season. Arrow.— OptaJoe (@OptaJoe) December 16, 2017
In-form Austin almost scored moments after his introduction as a second-half substitute, but the striker was denied by Courtois after running on to Pierre-Emile Hojbjerg's pass.
Hazard, who was playing as a false nine, thought he had scored his side's second after lashing in following a one-two with Fabregas, but a raised offside flag saw the goal disallowed.
Forster saved another effort from Alonso in the 71st minute and the goal-hungry defender then headed a Willian cross wide after substitute Alvaro Morata fired straight at the Saints keeper.
Courtois denied Austin again, the striker slipping at the vital moment and failing to get power on his poked effort, before Fabregas squeezed an effort narrowly wide from a tight angle after a cleverly taken quick free-kick.
Austin turned James Ward-Prowse's right-wing cross off target with five minutes to play as Southampton pushed for an equaliser, but Chelsea clung on for maximum points.
Key Opta facts:
- Chelsea have won eight of their last 10 games in the Premier League (D1 L1), including each of the last five at Stamford Bridge.
- Southampton have only won two of their 41 top-flight away matches against the reigning champions – they beat Leeds United in March 1970 and Chelsea in October 2015.
- Marcos Alonso has had a hand in 14 goals since his Chelsea debut (10 goals, four assists); more than any other Premier League defender.
- Southampton have made 25 changes to their starting XI over their last five Premier League games - in their previous 13 games this season they made 21 changes.