Victory in the Edinburgh derby was earned by goals from Hearts' three outstanding players - Rudi Skacel, Paul Hartley, with two, and Calum Elliot - and keeps them on course for Champions' League football next season, probably via the runners-up spot in the Scottish Premier League, although the title race is not over.
Celtic's stumble from 3-1 up to draw 3-3 at home to Dundee United on Saturday again highlighted their defensive frailties, allowing Hearts to close the gap on the leaders to eight points.
But what of Hearts' long-term stability and short-term fluctuations in form? Barring any testing last-minute bids in this transfer window - maybe from Southampton - they should retain Skacel and Hartley at least until the end of the season.
Losing either would seriously damage their championship hopes. Skacel laid on Hartley's opener after bustling work by Elliot. Then Hartley's free-kick eventually fell to Skacel, whose left-footed goal, his 16th of the season, made it 2-0. Skacel then earned the penalty that Hartley converted for 3-0, before Hibs were reduced to 10 men for Gary Smith's elbow on Saulius Mikoliunas.
Just after the break, Elliot scored the fourth. Garry O'Connor then got Hibs' consolation, although without a flurry of early saves by Hearts' Craig Gordon, it might have meant more.
Beyond this season, Skacel's future is uncertain. He is on a season-long loan from Marseilles, and Hearts have first option to sign him. However, Skacel has hopes of a World Cup place with the Czech Republic, and on Saturday it sounded like he wanted to use this summer's jamboree as a shop window.
"I'm not thinking ahead more than one match," he said of next season. "I want to help Hearts [do well now] and maybe Hearts will help me [get to the World Cup]."
As for Hearts' up-and-down form, their coach, Graham Rix, is as perplexed as anyone. Before he arrived in November, they had won 11 league games, drawn two and lost one. Since, they have won four, drawn three and lost three. Their blips, like defeat a week ago at Kilmarnock after a poor performance, are harming their hopes.
In what he said was a "beauty and the beast" screening before Saturday, Rix showed his players DVDs of the season's first Edinburgh derby (4-0 to Hearts in August) and the Kilmarnock match.
"I wanted to show them what they did wrong last week," Rix said. "I needed them also to see how good they were."
Goals: Hartley (27) 1-0; Skacel (41) 2-0; Hartley pen (44) 3-0; Elliot (50) 4-0; O'Connor (58) 4-1.
Heart of Midlothian (4-1-4-1): Gordon; Neilson, Webster, Berra, Fyssas; Brellier; Mikoliunas (Cesnauskis, h-t), Hartley, Johnson (McAllister, 77), Skacel; Elliot (Pospisil, 69). Substitutes not used: Banks (gk), Wallace, Tall, Mole.
Hibernian (4-4-2): Simon Brown; Whittaker, Caldwell, Smith, Murphy; Sproule, Stewart, Scott Brown (Fletcher, 40), Thomson; O'Connor (Killen, 79), Riordan (Konde, h-t). Substitutes not used: Marshall (gk), Hogg, McCluskey, Morrow.
Referee: M McCurry.
Booked: Hearts Brellier; Hibernian Murphy.
Sent off: Hibernian Smith (45).
Man of the match: Skacel.
Attendance: 17,371.Reuse content