Heiko Vogel's side moved on to eight points from five games, only a point behind Benfica and Manchester United who drew 2-2 at Old Trafford. The Swiss side must beat United in their last group game on December 7 to progress with the English champions needing a draw to reach the last 16.
"It's just great that everything will be decided at St Jakob Park," Vogel told reporters. "I'm so happy about the team and I want to congratulate everyone.
"We should've play better after we're 3-0 up but it showed once again why football is so spectacular and unpredictable."
The hosts, who have scored only once in the group, settled quickly at the National Arena, almost taking the lead after four minutes when Cristian Sarghi headed just over the bar from Laurentiu Iorga's cross.
After a relatively slow start, Basel broke the deadlock on a bitterly cold evening in Bucharest with their first attack when midfielder Fabian Frei gave goalkeeper Branko Grahovac no chance in the 10th minute with a powerful shot.
Four minutes later, Alexander Frei netted his fourth of the campaign with an easy finish from 10 metres following unselfish play from fellow striker Streller.
Otelul were far from lethargic but lacked ideas on how to create scoring opportunities with Basel, unbeaten away from home in the group, defending solidly.
Lively Xherdan Shaqiri went close to scoring a third midway through the first half but his curling left foot shot from the edge of the penalty area went just wide.
Basel captain Streller made it 3-0 eight minutes before the break after reacting quickly to a deflected clearance before racing through to slot past home Grahovac for his debut goal in the tournament this season.
Basel continued to play a neat passing game after the interval while Otelul failed to test young keeper Yann Sommer until the last quarter of ah hour.
Otelul finished strongly with captain Gabriel Giurgiu and Liviu Antal scoring in the space of six minutes but Basel were solid in defence in the dying moments and the Romanians suffered their fifth defeat in the group.
"I am disappointed," Otelul coach Dorinel Munteanu said. "It was a very poor first half for us as we made some mistakes you just can't afford at that level.
"We played better in the second half, the end was pretty good, and we even could've snatched a draw. The boys showed character in the second half."
In their final match Otelul travel to Benfica, who have already reached the knockout stages, on December 7.
