The Spain full-back ghosted clear in the box to nod home Willian’s teasing far-post cross, to hand the Blues the slender advantage midway through their quarter-final.
Chelsea came very close drawing their last-eight first leg tie at the Sinobo Stadium, the Blues struggling for fluency throughout a niggly night in Prague.
Replacement Ruben Loftus-Cheek’s smart spin and break turned Slavia’s defence at the death however, before Willian served up the perfect cross.
Alonso’s third goal of the season and second in the Europa League proved just enough for Chelsea then, but the Stamford Bridge men will hardly be happy with their performance.
Chelsea will now expect to complete the job and move through to the semi-finals when hosting Slavia in the return leg next Thursday.
The Blues were relieved to prevail on the pitch, in another night where racism hit the headlines.