Mahmoud Dahoud set up Christensen's first Bundesliga goal in the 31st minute and the 19-year-old Dane claimed his second in the 50th, with a header from Raffael's corner.
Claudio Pizarro pulled one back with a penalty six minutes later and Bremen put the home side under pressure.
Any hopes the visitors had of a comeback were dashed with 20 minutes to go when Raffael converted another penalty. Havard Nordtveit completed the scoring with a fine strike from distance in the 88th.
'Gladbach had started 2016 with two straight league defeats and had five defeats from its previous six competitive games.
"We clearly analyzed what needed working on, what needed to be done. We did it internally without going mad," said 'Gladbach coach Andre Schubert, whose side stayed fourth. "We corrected a few things. We stayed compact and were aggressive going forward."
Bremen remained in the relegation playoff place ahead of the rest of the 20th round of matches.
"We're in the middle of a relegation scrap. Everyone is compelled to defend the goal with everything they've got and we didn't do that today," Bremen captain Clemens Fritz said.
Bremen was missing ten players through injury or suspension. Hungarian midfielder Laszlo Kleinheisler made his first league start and Bremen reserve defender Leon Guwara was also named in the starting line-up for his Bundesliga debut.