Albiol got the second goal for Napoli eight minutes later with a header inside the box following a corner to seal three points and lock up second place, behind champions Juventus.
Needing just a draw to wrap up a 34th top flight title - to add to their Italian Cup won in midweek - Juve survived a bright Roma start which saw Edin Dzeko and Nainggolan fire over.
It has a four-point lead over Napoli with one round left.
And their coach believes this had an impact, pinpointing a key defeat at Fiorentina the day after Juventus - beaten by Napoli in their previous match - had conjured up a late comeback against Inter.
Juve could not capitalise, although they were content with the point as Allegri's side completed the double just days after their 4-0 victory over AC Milan at the Stadio Olimpico. Meanwhile, they might be one of Europe's most successful teams, but it's more than 20 years since they were crowned champions of Europe.More news: Gap Apologizes for Selling T-shirt with 'Incorrect' Map of China
"Behind their successes there is a mentality which has been built over the years", Roma coach Eusebio Di Francesco said.
"It's a club that succeeds in remaining united through difficulties".
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A number of players could leave Juventus at the end of the season, notably club captain Gianluigi Buffon, although the veteran goalkeeper has yet to confirm his retirement.
Emanuele Giaccherini and Roberto Inglese scored in the second half to rally Chievo to a 2-1 win at Bologna.