Puel made seven changes to the team that on Saturday lost 2-1 at Arsenal. He was regardless rewarded, however, with two goals from the recalled Charlie Austin and another from sub Jay Rodriguez.
Making only his second start of the season — Austin had been expected to benefit from the departure of Graziano Pelle to China’s Shandong Luneng — the striker won a fifth-minute penalty when his low right-wing cross struck unlucky Sparta defender Costa Nhamoinesu’s elbow.
A brief argument with Dusan Tadic over who would take it ensued, before Austin struck into the left corner beyond Tomas Koubek.
In the 26th minute when, following positive build-up play from Shane Long, Austin dived low to head home.
Southampton played with less intensity in the second half but Rodriguez combined with Long, before finishing with ease in the last minute.
Forster, Martina, van Dijk, Targett, Yoshida, Hojbjerg, Romeu (Davis 83), Ward-Prowse, Tadic (Redmond 70), Austin (Rodriguez 76), Long.
Koubek, Holek, Nhamoinesu, M Kadlec, Karavaev, Frydek, Sacek, Vacha (Marecek 64), Sural (Pulkrab 74), V Kadlec, Julis (Lafata 47). Ref: Manuel Grafe (Germany).