The 26-year-old found the net inside 22 seconds at Borussia-Park, slotting home a fine pass from returning strike partner Niclas Füllkrug.
The goal was Wood's third in 10 Bundesliga appearances following his summer loan move to Hannover from Hamburg. He grabbed a brace in the 3-1 win over VfB Stuttgart on Matchday 7, and has now scored more times than he did in 24 games for HSV last term.
Watch: Relive Bobby Wood's first Bundesliga goals for Hannover
Wood, who began his professional career with 1860 Munich, has also played for Erzgebirge Aue and Union Berlin. The 45-time USMNT international has scored 10 times in 62 Bundesliga appearances to date, as well as 23 in 90 outings in Germany's second tier.
Whilst playing for Union in Bundesliga 2 in 2015/16, he set a single-season record for most goals by an American (17).