Victory saw Steven Gerrard's men capitalise on the fact that reigning champions Celtic, the Gers' bitter Glasgow rivals, could not hold on to a lead earlier Sunday when Aberdeen snatched an injury-time equaliser in a 3-3 draw at Pittodrie.
Rangers have now established a clear gap between themselves and second-placed Celtic, who are bidding to become the first side to win 10 successive Scottish titles -- both the Hoops (also in 1965-74) and Rangers (1988-97) have previously managed nine in a row.
After Joe Aribo put Rangers in front at Ibrox, Defoe struck in the 16th minute with his landmark goal -- also the much-travelled 38-year-old's first in league football this season.
The former England striker, who scored his first goal in senior football with West Ham 20 years ago last month, received a ball over the top from James Tavernier, got in between Livingston's centre-backs and did not break stride with a left-foot finish.