An even contest between the two favourites for progression from Group E produced plenty of chances, but neither side could apply the finishing touch necessary to claim all three points.
Rennes' draw with FK Krasnodar in France meant that it was honours even across the group following the first matchday.
Chelsea's leaky defence had come in for scrutiny once again following a weekend Premier League outing that saw it held to a 3-3 draw by Southampton.
And head coach Frank Lampard's nerves will not have been helped by Thiago Silva's failure to make a seemingly simple headed clearance during an early passage of play that led to a Lucas Ocampos shot, albeit from a marginally offside position.
Sunday's (AEDT) result had no doubt contributed to a defensive reshuffle that saw Edouard Mendy replace Kepa Arrizabalaga in goal among other changes.
The potential value of that particular switch was shown after 18 minutes when the Blues' recent signing was on hand to claw away a Nemanja Gudelj header that had been diverted goalward by a deflection off Kurt Zouma.
At the other end, Chelsea evidenced their own threat when Timo Werner produced his team's first shot on target following a sweeping move involving the lively Reece James.
Still, it could not entirely limit Sevilla, which came close through a Suso header following brilliant work from Marcos Acuna and an Ocampos shot that needed a Mendy save just prior to the whistle sounding.
Although Lampard opted against making substitutions at the break, a tactical tweak that saw Christian Pulisic move from the right side to the left almost paid immediate dividends.
The American's quick feet earned Chelsea a corner that saw Zouma head on target, and he followed that with another dangerous cross from his preferred flank just seconds later.
With Pulisic benefiting from a direct approach, the Blues called for more thrust on the opposite wing with an hour gone as Hakim Ziyech replaced the ineffectual Mason Mount.
But their opponent was by no means ready to give up its share of the points and went close itself when Joan Jordan showed great technique in volleying just over the bar from a corner.