The Frenchman opened the scoring for Mauricio Pochettino's men when he headed home after Rickie Lambert set him up from a Nathaniel Clyne cross.
Lambert went on to double the tally on the half-hour mark before Adam Lallana gave the hosts a comfortable 3-0 half-time lead.
The Tigers bit back after the break when Yannick Sagbo struck beyond Artur Boruc but substitute Steven Davis secured the points late on with Southampton's fourth.
Despite the second-half blemish, Schneiderlin is delighted to see Saints enter the international break on an eight-match unbeaten run.
"It is very nice to get to the international break with a win," he told Sky Sports.
"We're happy we did everything in the first half to get the game in bed with three good goals.
"It's really difficult when you have three goals to keep going, to keep attacking to get the fourth and we conceded a goal poorly.
"I think after that we stayed strong and scored the fourth, that was game over."
Schneiderlin celebrated his 24th birthday on Friday and admitted scoring his first goal of season was the ideal way to celebrate but also dedicated the win to injured team-mate Guly do Prado.
"I'm very happy," he said. "To finally get on the score-sheet, it was a long time I didn't score, but I am very happy.
"I would like to give this goal to Guly do Prado, he has had an operation on his knee and the goal and the win are for him."
England manager Roy Hodgson watched on from the stands after selecting Lallana, Lambert and Jay Rodriguez for the upcoming fixtures and Schneiderlin heaped the praise on his Saints team-mates after they vindicated their selection.
"I've had the chance to walk with him for six years, growing as a player, he's just fantastic, so much ability," he said of Lallana.
"I think he's one of the best talents in England and he deserved that call-up, today he showed that he deserved that."