Brazilian star Kaka gave the visitors the lead in the 13th minute at Parkhead, with Cristian Zapata and Mario Balotelli putting the result beyond doubt in the second half.
The result left the Rossoneri second in Group F, one point clear of Ajax and two behind pool leaders Barcelona with one game remaining.
"This victory is very important for many reasons," Emanuelson said to www.acmilan.com.
"We had not won for seven straight games, which is something incredible for a team like Milan.
"But we know what we need to do in order to improve.
"We hope we can continue on this path and we can do well against Catania on Sunday."
Coach Massimiliano Allegri had gone into Tuesday's game under pressure to secure a win, knowing that any other result could have seen him lose his job.
Milan have endured their worst start to Serie A in three decades, having taken just three wins in 13 games.
"This victory is not just for Allegri but for the whole team," Emanuelson said.
"It's an important win at a difficult time for us."
Milan host Emanuelson's former club Ajax in the last group game on December 11 knowing that anything but a defeat would see them join Barca in the last 16 of the Champions League.
"We hope we can produce the same performance against Ajax," Emanuelson said.