The Jambos lead Rangers, who thrashed Aberdeen 4-1, by three points with seven games remaining.
Celtic are now five points off the top but have a game in hand on both their title rivals away at Dundee United on Sunday.
Defeats in their last three away games have stalled Hearts' charge towards their first title in 66 years and becoming the first non-Old Firm winner of the league since Aberdeen in 1985.
However, their home form has kept them in front in the title race.
Hearts were boosted by the return of captain Lawrence Shankland from injury as a second-half substitute.
But it was defender McEntee who made the breakthrough as Derek McInnes' men again relied on their strength from set-pieces.
The Northern Irishman powered home a header from Marc Leonard's free-kick 13 minutes from time.
Hearts then had to see out the final few nervous minutes a man down when Frankie Kent was shown a second yellow card.
"We've been tested of late, but despite all that, we're going to be top of the league in April," said McInnes.
"We're huge underdogs, but for us still to be where we are, churning out victories, as we did again, there's a lot to be said for 1-0 victories."
Rangers responded to Hearts' win earlier in the day with a dominant display against struggling Aberdeen.
Tochi Chukwuani fired the home side into a half-time lead from the edge of the box.
Tottenham loanee Mikey Moore curled in a second just after the break before a defensive mix-up gifted the Dons their first away goal since December through Dennis Geiger.
Nico Raskin quickly restored Rangers' two-goal cushion before James Tavernier rounded off the scoring with a stunning free-kick in stoppage time.
Defeat leaves Aberdeen just three points above the relegation play-off place.