The Swiss side, who dropped into Europe's second-tier competition after exiting the Champions League before Christmas, were never in any danger of relinquishing the slight advantage they gleaned from a goalless first leg, as a Valentin Stocker goal and Marco Streller's brace saw them through.
Maccabi rarely threatened in the course of a lacklustre 90 minutes, although the Israelis at least have the comfort of knowing Basel cannot cause them any further hurt this season having already lost to the Swiss champions in the third qualifying round of the Champions League back in August.
A far tougher assignment lies in wait for Basel, however, with Austrian outfit Salzburg - so impressive in routing Ajax 6-1 in the last 32 - their opponents in the next round.
Basel bossed the early possession on Thursday night and took the lead in the 18th minute with the first presentable chance of the contest, Behrang Safari the provider with a centre from the left which was met with a firm header into the left corner by Stocker.
Listless Maccabi failed to produce a response and nearly fell further behind in the 42nd minute when Stocker flashed an effort wide of the post from close range.
Maccabi finally came to life shortly before the hour when Rade Prica's shot was blocked by Arlind Ajeti and Maharan Radi saw his follow-up clawed away by Yann Sommer.
The hosts immediately capitalised on that escape by extending their lead on the hour, Serey Die's cross finding Streller who made no mistake with a headed finish.
And the result was put beyond any doubt in the 71st minute as yet another header undid the Maccabi defence, this time Stocker the provider for Streller to guide the ball into the right corner.