After Carlos Soler hit the bar for West Ham early on, Paul Onuachu had the first clear chance of the Jurić era, only for him to head narrowly wide.
Another golden chance then went begging just before the 20-minute mark, with a Mateus Fernandes header from Adam Armstrong saved well by Łukasz Fabiański.
Southampton kept coming forward with their newfound vigour, but Fabiański produced a top-drawer fingertip save to keep out another Onuachu header – this one bound for the top-left corner before the Pole’s intervention.
However, the West Ham keeper’s afternoon would soon be cut short by a nasty-looking head injury sustained in an aerial duel with Nathan Wood. A 10-minute delay for medical attention ended with the Polish stopper being stretchered off.
His replacement Alphonse Areola didn’t have much to do in the glut of added time created by that stoppage, though Onuachu still had enough time to put a header straight at him just before the break.
Early in the second half, West Ham’s Guido Rodríguez was shown a straight red card for a two-footed challenge on Kyle Walker-Peters as he broke forward. However, a VAR review showed that he still had both boots with studs on the turf, leading to the punishment being downgraded.
And frustration then became despair for Southampton, when West Ham took the lead on the hour mark. Taylor Harwood-Bellis was the instigator, twice failing to clear from a corner, allowing a succession of passes that allowed Tomáš Souček to play a ball into the box.
Practically under the nose of Aaron Ramsdale, Niclas Füllkrug flicked the ball across to Bowen, who fired in a simple close-range effort.
West Ham now needed only to keep it tight at the back in order to make that goal Bowen’s fourth matchwinner across six scored this campaign.
But their goal lived a charmed life as Southampton gained a second wind, which saw Walker-Peters play in Fernandes, who fired a low shot just inches wide, just moments before Crysencio Summerville broke down the other end and went similarly close from a narrow angle after cutting inside on his right foot.
While there was a late salvo of missed chances for West Ham to resist, the Saints simply couldn’t land anything on target. With their defence staying resilient and disciplined throughout the dying minutes, West Ham held firm to claim only their second win in eight away games.
The Hammers celebrated with all due gusto, but it could get worse for Southampton after another day to forget, with adverse results elsewhere later on potentially seeing them enter the final weekend of 2024 a whole 11 points adrift of safety.