Steven Whittaker made a darting run deep into Hearts territory, before proceeding to clip the ball into the path of Lafferty, who delightfully smashed it home low and on the volley past a hapless Marian Kello in the Jambos goal.
It was the perfect start for Rangers, as Lafferty's sixth goal of the season settled any pre-match nerves amongst the Ibrox faithful.
Neither side had really built up sufficient rhythm in what proved to be a cagey opening first 45 minutes.
Following the goal, Hearts looked to control the middle of the park through Spanish duo Ruben Palazuelos and Suso Santana.
However, they lacked the necessary penetration to trouble Rangers - something which was particularly evident in the shape of Rudi Skacel's wasteful 35-yard effort in the 17th minute.
Indeed, the only real Jambos chance of the half came from their captain Marius Zaliukas in the 28th minute.
A curled free-kick from Craig Thomson was headed towards the Rangers goal by Zaliukas, but Allan McGregor was equal to it, producing a fine fingertip save to keep the home side's lead intact.
Rangers were forced into a 20th minute substitution as El-Hadji Diouf entered the action; replacing Lee McCulloch who had taken a knock and subsequently being greeted with a warm reception on his debut.
Diouf proceeded to link up well with Vladimir Weiss as the first-half clock ran down, but what was becoming more noticeable was the frequency with which Hearts players were entering into the referee's book.
Santana, Zaliukas, Ian Black and Eggert Jonsson were all carded as Jim Jeffries' side grew frustrated at sloppily giving possession away to Rangers on more than one occasion.
Into the second half, and Rangers began the brighter with a flowing interchange of passes that lead to a flick on from Steven Davis into the path of Madjid Bougherra in the 51st minute.
Bougherra struck low from inside the Hearts box, but Kello was on hand to beat the ball away at his near post.
Then, just past the hour mark, Diouf picked out Maurice Edu at the Hearts back post with a pinpoint cross.
However, the American took too long to control and manoeuvre the ball onto his favoured right foot for the shot, and the opportunity was consequently lost.
Hearts offered little in the final third and their attacking play was looking increasingly laboured as time passed by.
Even the introductions of Ryan Stevenson, who scored in the Tynecastle club's 1-0 victory over Rangers eleven days ago, Andrew Driver and Gary Glen failed to stir Hearts' spirits.
And that meant that Rangers, who had a second goal chalked off after Steven Davis was adjudged to have drilled home from an offside position in the 90th minute, were able to comfortably see their way through to full-time with their one-goal lead intact.
Three points secured then and Walter Smith's men now move to within five points of league leaders Celtic, having played two games less, with a mouth-watering Old Firm clash in the Scottish Cup to come on Sunday.