A 15th minute effort from midfielder Simone Perrotta enabled Roma to match the runs put together by Juventus in 1931-32 season, AC Milan in 1950-51 and Bologna in 1963-64.
Totti was carried off in the 12th minute after a heavy challenge by Empoli defender Richard Vanigli.
The Italy international is expected to be out of action for about two months.
The win gave Roma 51 points from 26 matches and moved them up to fourth - Italy's final Champions League berth.
They are one point ahead of Fiorentina, who slipped back to fifth after losing 2-1 at home to Lazio.
Juventus lead the division on 67 points after a 2-2 draw with Messina on Saturday.
Roma struggled to produce their usual fluent football and owed their 15th-minute winner to a howler by goalkeeper Sebastian Cejas, who spilled Antonio Busce's backpass into the path of Simone Perrotta, who tapped in from close range.
Midfielder Daniele De Rossi wasted a chance to extend the lead just before halftime when he scuffed a loose ball inside the area, a mistake that almost cost Roma in the 50th minute when Empoli striker Nicola Pozzi put the ball wide from close range.
Roma can set a record of 11 consecutive wins by beating Lazio in the Rome derby next weekend.
Their city rivals did Roma a favor on Sunday by beating Fiorentina at the Stadio Franchi. Before today, Fiorentina had won all but one of their 13 home matches this season.
They fell behind in the 32nd minute when Lazio winger Valon Behrami turned his marker on the edge of the area, held off Per Kroldrup and angled the ball past Bogdan Lobont.
Lazio extended their lead four minutes after the interval, midfielder Fabio Liverani conjuring up a perfectly-weighted chip over Fiorentina's defence for Tommaso Rocchi to head in.
A lively last half hour by Fiorentina produced a superb consolation goal by Valeri Bojinov, who unleashed a volley that dipped under the crossbar from 25 metres out.
The win moved Lazio up one place to eighth on 38 points, one point behind Chievo Verona, who drew 0-0 with Palermo.
CNN: http://www.cnn.com
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