Alonso had switched off to help James Maddison to rifle the Foxes into an early lead at Stamford Bridge, but delivered a sweetly-struck effort to level before the break.
The Blues boast a three-point advantage on fourth-placed Tottenham going into the campaign’s final day, but a goal difference superiority of 18.
Christian Pulisic inexplicably missed a tap-in that would have sealed third place for the Blues with a game to spare.
The USA forward scuffed wide when it was far easier to score, and so Chelsea were left to finish the job in Sunday’s final match of the season against Watford at Stamford Bridge.
Todd Boehly was at Stamford Bridge again, but of the matches it is known the incoming new owner has attended, the US magnate has yet to see Chelsea win in person.
Boss Thomas Tuchel and his players would have been frustrated not to convert at least one of several big second-half chances and seal victory.
The tie was played out in front of a curiously subdued Stamford Bridge, with the home supporters perhaps fatigued by the continued takeover saga.
But the Chelsea fans unveiled a banner in tribute to manager Tuchel before kick-off, and the beaming German coach appeared delighted with the support.
Chelsea moved the ball around neatly from the off, but failed to open Leicester up.
Maddison made the Blues pay with a rifled finish from 18 yards, punishing Alonso’s failure to track back.
Kasper Schmeichel’s raking ball should not have dropped to Timothy Castagne, but Alonso had switched off and missed the danger.
The full-back’s inside pass flicked off Toni Rudiger’s heel, and Maddison latched onto the loose ball before lashing past Edouard Mendy.
Romelu Lukaku fluffed a fine chance when played in by N’Golo Kante, with the Belgium hitman delaying his shot too long.
Chelsea finally levelled though, when James’ masterful diagonal cross was matched by Alonso’s crisp volley.
After the sides had turned around on level terms, Chelsea set to work on taking control.
While the Blues seized the initiative however, they kept failing to turn their dominance into a lead.
Lukaku nodded wide from Hakim Ziyech’s smart cross, and then Christian Pulisic side-footed wide with the goal at his mercy.
James and Lukaku contrived to deliver a tap-in on a plate for the USA forward, but he could only scuff wide.