Uncertainty in the Gladbach back four put first-half goals on a plate for Antonio Candreva and Alvaro Gonzalez as Lucien Favre's men succumbed to a disappointing 5-3 aggregate defeat.
Gladbach shot themselves in the foot just nine minutes into the contest when a poor touch on the edge of his own area from defender Alvaro Dominguez gifted possession to Candreva. The Lazio midfielder needed no invitation and calmly raced away to slot past a helpless Marc-Andre ter Stegen and put the Italians back in the driving seat.
An uncharacteristic mistake from the Foals stopper almost let Gonzalez in for Lazio's second, but it wasn't long before the 20-year-old was once again having to fish the ball out of the net. Stefan Radu's fizzing drive drew a sprawling save from the Gladbach no1 and, with Oscar Wendt ball watching, Gonzalez pounced to tuck away his side's second of the night.
Done and dusted
Favre responded by sacrificing Juan Arango for Amin Younes shortly after the restart, but the move did little to change the one-sided nature of the tie. Striker Luuk De Jong cut a lonely figure in the lone striker's role and when Gladbach did manage a shot on goal, roaming centre-back Martin Stranzl could only find the arms of Federico Marchetti.
To their credit, the Foals kept plugging away as the clocked ticked on. Patrick Herrmann was seeing much more of the ball in advanced positions, but try as he might, the sprightly midfielder was unable to give the 10,000 travelling fans the goal their vociferous support so richly deserved.
Gladbach: ter Stegen - Jantschke, Stranzl, Dominguez, Wendt - Marx, Cigerci (Hanke 69'), Nordveit, Hermann - Arango (Younes 52'), de Jong
Lazio: Marchetti - Konko, Biava, Cana, Radu - Candreva (Pereirinha 83'), Ledesma, Hernanes- A. Gonzalez (Onazi 69'), Lulic - Floccari (Kozak 79')
Goals: 1-0 Candreva (10'), 2-0 Gonzalez (33')