The Swiss side took a first-half lead through Fabian Frei before Marius Pena levelled for the Romanians just before the hour in the Group C game.
Otelul were worth a point until Marco Streller was judged to have been fouled in the penalty area and Frei, the Swiss national team's record goalscorer, stepped forward to convert the penalty in the 84th minute.
Neither team offered much to suggest they could pose a threat to Manchester United and Benfica, the other teams in the group and favourites to qualify.
A dull opening half hour saw only one scoring chance when Basel midfielder Granit Xhaka's low drive was parried by Branko Grahovac.
The hosts went ahead five minutes later when Streller cleverly beat his man on the right and produced an inviting cross for Fabian Frei to head into the bottom corner.
Otelul, whose coach Dorinel Muneanu is Romania's most capped international, fired a couple of warnings early in the second half as John Ibeh's shot was saved by Yann Sommer and Liviu Antal was close with a dipping long-range effort.
They levelled in the 58th minute when Antal's low shot was saved by Sommer and Marius Pena followed up to slot home the rebound.
Otelul's Adrian Salageanu was sent off in the incident which led to the penalty and Basel captain Benjamin Huggel was dismissed in the 86th minute.
