Champions Sarries have now collected more points this season than Exeter, but a 35-point deduction for breaching salary-cap regulations means they remain bottom of the pile and in the red.
However, the beleaguered the London club is making swift progress in its survival bid and scored 10 tries in rout of Worcester at Allianz Park in a week that saw Nigel Wray resign as chairman.
It was one-way traffic from the outset as Ben Earl opened the scoring after six minutes, with the first of Rotimi Segun's first-half double coming quickly thereafter.
Brad Barritt and Mako Vunipola also went over before the break, and Sarries matched their haul from the first 40 minutes in the second period.
Richard Barrington, Maro Itoje, Duncan Taylor, Jackson Wray and, finally, in the 81st minute, Elliot Daly got on the scoresheet, with Owen Farrell nailing six conversion attempts.
There was a derby win for Gloucester as it put on a late show to beat Bath 29-15 at Kingsholm.
Rhys Priestland's five penalties had visitors Bath in front until just before the hour-mark, but tries from Gerbrandt Grobler and Ruan Ackermann in quick succession set up an ultimately comfortable victory.
Leicester got a much-needed win as it saw off Bristol Bears 31-18, led by England pair George Ford and Jonny May.
The Tigers are only kept off the bottom of the table by Sarries, but a strong start set up a precious second victory of the season in the early kick-off.
Bristol-born Ellis Genge England prop went over with just three minutes played, and May and Ford crossed later in a first half that saw two Bears men sent to the sin bin.
Although Bristol battled back early in the second period, May had his second try with six minutes remaining, while Ford dispatched all four conversions and a penalty to leave Leicester 18 points better off than European Champions Sarries.