With Celtic toiling, Rangers building momentum, and a favourable run of fixtures this month, this felt like a must-win game for Hearts.
In the first period they played like a team who believe they can be champions as they bossed their struggling opponents off the pitch.
New signing Altena created three chances, including a brilliant ball in for Halkett to head in his sixth goal of the season, and looked promising going forward.
Fit-again midfielder Beni Baningime strolled the opening 45 minutes as Cammy Devlin put in another towering performance, and Lawrence Shankland floated about causing mayhem.
The Scotland striker laid on six opportunities overall, the most he has created in a league game for two-and-a-half years.
All of that should have resulted in a comfortable half-time scoreline, but instead Livingston took confidence from still being in the game.
They went direct in the second half as Mohamed Sylla started to get into the game, and Yengi was outstanding as he busied himself in the final third.
The striker had three efforts in good positions saved by Schwolow, the best of them after turning inside Stuart Findlay in the box.
At the end Hearts had to stand up to a strong challenge and a nervousness in their own stadium as McInnes brought on more defenders to see out an important win.
All that matters is they got it and now have a six point advantage at the league summit again.