A pulsating clash exploded into life at the start of the second half with both sides spurning decent chances before Hamsik twisted, turned and then rifled a left-foot shot into the far corner to open the scoring in the 52nd minute.
Lazio struck back almost immediately, Keita's shot squirting under the body of Pepe Reina for the equaliser two minutes later.
The point keeps Lazio in fourth place on 22 points alongside third-placed AC Milan, who play at Palermo on Sunday.
Juventus, who visit Chievo Verona on Sunday, are top on 27 points, four ahead of Roma, who host Bologna. Napoli are now fifth on 21 points.
Napoli had enjoyed much of the possession in a scoreless first half, with Hamsik pulling the strings in midfield and Napoli's attacking trio of Lorenzo Insigne, Dries Mertens and Jose Callejon pinning back Lazio for long spells.
After the goals, Napoli pressed forward and substitute Manolo Gabbiadini, on for Insigne, had several opportunities to put his side ahead again, but Lazio keeper Federico Marchetti made a series of smart saves to keep the scores level.
Maurizio Sarri's side continued to press forward looking for the winning goal, but with Insigne, Callejon and Hamsik all replaced they failed to find the spark they needed and Lazio held on for the draw.
Earlier, Andrea Belotti scored twice as Torino hammered Cagliari 5-1 with Danielle Baselli capping off a miserable day for the visitors by conceding a penalty and getting sent off on the hour mark.
(Reporting by Philip O'Connor; Editing by Ian Chadband)
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