Sadio Mane scored his seventh goal in five games before a late defensive error from Virgil van Dijk allowed Ryan Babel to equalise for Fulham, but Milner was on hand to steer in an 81st-minute decider.
Jurgen Klopp's side have again played one game more than City—who beat Swansea City 3-2 to move into the FA Cup semi-finals on Saturday—but will nonetheless cherish their two-point lead at the summit.
There was a period of play soon before Fulham's equaliser when Klopp's visitors looked vulnerable, and tensions were evident as their narrow lead threatened to leave them open to dropping more points.
The hosts capitalised on those nerves, and it seemed almost fitting the prides of their defence—star defender Van Dijk and goalkeeper Alisson—were the pair at fault for Fulham's equaliser.
Their misunderstanding in communication coupled with a somewhat awkward bounce was enough to let Babel sneak in and score in an open net, via NBC Soccer (U.S. only):
January arrival Babel refused to celebrate against his former club, via Soccer AM (UK only):
Though Alisson has had a few wobbles in his first season on Merseyside, he and Van Dijk have been largely reliable as Liverpool have assembled the best defence in the division. They've conceded a league low of 18 goals this term, three fewer than City.
However, a tally of seven draws sees them sitting a close second to Pep Guardiola's side. While City have lost four times to Liverpool's one, those 14 dropped points have come largely because of their switch to a more defensive approach.
It's worth noting fatigue was likely a factor for the Reds after beating Bayern Munich to advance to the UEFA Champions League semi-finals only four days earlier.
Klopp spoke to Sky Sports before Sunday's narrow victory and was confident of his side's chances in west London despite the tight schedule:
That's not to say a team that's scored nine times in their last three matches isn't capable of the same devastation showcased more frequently last season, but the change in paradigm seems evident. The change from a more cutthroat—albeit riskier—mentality could pay dividends, or it could hamper Liverpool.
City have scored 79 times in 30 matches and are on course to challenge last season's Premier League record-breaking total of 106 goals. Liverpool have scored 68 and will be wary of chasing down City's advantage in goal difference, lest it sees them drop points and out of the race altogether.
It doesn't help their cause that star man Mohamed Salah has scored only once in nine games, but Mane has stepped up of late to give them at least one reliable finisher in attack:
Klopp will hope Van Dijk and Alisson have seen the last of their big mistakes in attack, with too much of Sunday's game spent in a state of suspense as Liverpool's title hopes lie on the line.
Ironic as it might be, it could transpire that Liverpool's new focus on defensive strength could stand in their way of cutting down City's advantage at the top.
The Premier League will pause for the international break, but Liverpool return to action at home to Tottenham Hotspur on Sunday, March 31. Fulham will look to avoid an eighth straight defeat at home to Manchester City on Saturday, March 30.