A header from Andrius Velicka ended Hearts' 10-game run without a win and claimed the Edinburgh derby honours.
The Lithuanian's nod from six yards after 20 minutes was straight at Yves Ma-Kalambay but the Hibs keeper could only flap the ball into his own net.
With both sides struggling at the wrong end of the table, there was a real shortage of quality play.
However, Hearts posed more threat in attack, while Hibs seldom caused the home defence any trouble.
Hearts will be delighted with a rare victory and to have kept just their second clean sheet of the season.
Hibs, who last won a league game on 10 November, saw a lot of the ball in the second half but could not craft any meaningful chances.
A congested midfield and some typically robust tackling made for a scrappy opening but Hearts looked the more menacing side, with the visitors frequently gifting them possession.
With 11 minutes gone, Ruben Palazuelos rode a poor tackle from Hibs skipper Rob Jones on the edge of the penalty box and his deflected shot was brilliantly clawed away by Ma-Kalambay.
Hibs countered with a quick break but Abdessalam Benjelloun's shot on the turn from 18 yards was easily gathered by Steve Banks.
Another deflected strike troubled Ma-Kalambay but Eggert Johnsson's powerful effort looped narrowly wide of the target.
The opening goal came via a deep corner kick, which was nodded back into the danger zone by Christophe Berra, and Velicka's close range header was fumbled over the line by Ma-Kalambay.
Hibs winger Filpe Morais fizzed a low delivery across the Hearts penalty area but Benjelloun completely missed the ball with a swipe when he was perfectly placed to score.
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Fellow Moroccan Merouane Zemmama then had a shot blocked by former Hibee Michael Stewart, who was guarding the post from a corner.
Hibs were growing as an attacking threat but a swift counter from the home side saw Andrew Driver's low strike saved by Ma-Kalambay and Hearts were once again in the ascendancy as the first half drew to a close.
The visitors made a bright start after the interval and had Hearts pinned back for long spells, although Banks was not called into action thanks to some resolute defending from his team-mates.
Hibs were also undone by poor decision making and the final ball from midfield often left the forwards frustrated.
Half time replacement Steven Fletcher, back from a lengthy injury lay-off, did engineer some room on the edge of the penalty box after 73 minutes but his shot was well blocked by the lunging Johnsson.
Hearts came close to a late goal when substitute Saulius Mikoliunas was presented with a free header in a central position but Ma-Kalambay got down smartly to keep it out.
And there was another scare for Hibs when full-back Kevin McCann shaved the outside of his own post with a clearance.
Hearts: Banks, Neilson, Karipidis, Berra, Goncalves, Jonsson, Stewart (Wallace 65), Palazuelos (Nade 81), Driver, Velicka, Cesnauskis (Mikoliunas 70). Subs Not Used: Bjornsson, Thomson, Beniusis, Ksanavicius.
Booked: Velicka, Driver, Nade.
Goal: Velicka 20.
Hibernian: Ma-Kalambay, McCann, Hogg, Jones, Murray, Morais (Gray 81), Kerr, Beuzelin, Zemmama (Rankin 68), Benjelloun (Fletcher 46), Shiels. Subs Not Used: McNeil, Chisholm, McCormack, Hanlon.
Booked: Jones, Beuzelin.
Att: 17,131
Ref: K Clark
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