Diomande dazzles as Leipzig go two points behind Bayern
Leipzig returned to second spot after Dortmund had leapfrogged the Red Bulls with a 1-0 win at Augsburg on Friday.
Leipzig captain David Raum said his side were "only focusing on ourselves" despite edging closer to Bayern, but added: "We don't have to hide the mentality and the momentum we currently have."
Leipzig and Stuttgart enjoyed several chances in an exciting opening half before Diomande forced a breakthrough just before halftime.
The 18-year-old Ivorian dribbled down the right and delivered a low cross which Stuttgart defender Jeff Chabot turned into his own net.
Eight minutes into the second half, Diomande danced through three Stuttgart defenders before blasting a low shot into the bottom corner.
Tiago Tomas scored for Stuttgart to cut Leipzig's lead but Romulo made sure of the win when he pounced on a error from visiting goalkeeper Alexander Nuebel and tapped home.
Leipzig were thumped 6-0 by Bayern in their league opener but since then have claimed 22 of a possible 24 points in the league.
League leaders Bayern can return the gap to five points with a win at home against Bayer Leverkusen later on Saturday.
Diomande was one of an array of talented newcomers to join Leipzig in the summer as the club focused on youth in Jurgen Klopp's first transfer window as football coordinator of Leipzig's parent company Red Bull.
Eintracht Frankfurt's struggles continued with a 1-1 draw at last-placed Heidenheim, days after Dortmund booted them out of the German Cup.
Frankfurt's Danish defender Rasmus Kristensen scored in the second half to cancel out Budu Zivzivadze's opener.
The draw leaves Eintracht in sixth, having won just once in their past seven matches in all competitions.
Union Berlin and Freiburg played out a scoreless draw in the German capital, with both sides having goals struck off by VAR.
Elsewhere, Borussia Moenchengladbach won their first Bundesliga game since March with Haris Tabakovic bagging a brace in a 4-0 victory at St Pauli.
Jens Stage scored an equaliser with four minutes left as Werder Bremen snatched a 1-1 draw at lowly Mainz.