The victory extended Spurs' unbeaten home run in European competitions to 19 matches, but injuries to key players Maddison and Dominic Solanke cast a shadow over the night.
The match exploded into life after just 38 seconds when Brennan Johnson nodded in a header from Richarlison, who latched onto Pedro Porro's deep cross following Yves Bissouma's tenacious midfield work.
"We wanted to set the tone early," Ange Postecoglou said post-match. "The lads executed that perfectly."
Maddison doubled the lead on 34 minutes, showcasing his class with a deft touch to control Porro's pinpoint long ball before a scuffed finish fooled Bodo/Glimt's goalkeeper Nikita Haikin. "It wasn't the cleanest strike, but they all count," Maddison said on social media after the game.
Solanke added a third from the penalty spot just before the hour mark, coolly converting after Fredrik Sjovold's clumsy foul on Cristian Romero.
However, the mood shifted as both Maddison and Solanke were forced off in the second half with knocks. Maddison felt a "tweak in his knee," while Solanke reported discomfort in his quad.
"Madders and Dom didn't feel anything too serious, but we weren't taking chances," Postecoglou said. "We'll assess them over the next few days." Recent updates from Tottenham's official X account confirmed both players are undergoing scans, with no further clarity on their availability for the second leg.
Bodo/Glimt clawed back a late goal through captain Ulrik Saltnes, whose deflected effort wrong-footed Guglielmo Vicario with seven minutes remaining. The strike offered the Norwegian champions a lifeline ahead of the return leg on their artificial pitch near the Arctic Circle.
"It's a tough place to go, but if we replicate this discipline and intensity, we'll be hard to stop," Postecoglou said, drawing on his experience managing Celtic at Bodo's Aspmyra Stadion.
Tottenham's injury woes deepened with news that Lucas Bergvall, recently re-signed to a long-term deal, suffered an ankle injury in training. "It's a blow for Lucas after such a strong season," Postecoglou said. "We'll know more soon, but it opens the door for someone else." Bergvall was spotted on crutches, and Spurs' X account noted he's "undergoing further evaluation."
Despite the setbacks, Tottenham hold a two-goal cushion and a formidable European home record. Bodo/Glimt, however, remain a threat, having won all three home legs in this season's knockout rounds. "We know what's coming," Postecoglou said. "It's about staying focused and delivering again."