Despite the 2-0 scoreline this was a one-sided contest with Walter Smith’s side cruising to victory and Allan McGregor rarely troubled throughout the 90 minutes.
Lafferty and Boyd were the goal heroes for the Gers but it was new signing Mendes that stole the show with an excellent debut.
His performance was as you would expect; tidy, inventive and also full of graft.
Indeed, the Portuguese international, who has been handed the no. 4 jersey, was at the heart of Rangers’ early attacks.
On 6 minutes the hard-working Lafferty cut inside from the left flank but his right-foot shot from 20 yards was off target. This however, was a sign of what was to come.
Boyd then had a chance to open the scoring minutes later.
Mendes chipped the ball forward and Velicka flicked it on with his head, taking a hefty knock in the process.
The Gers’ no. 9 had space and time but his attempted chip over Jamie McDonald did not have the height or power and the Jambos’ keeper gathered the ball easily.
Rangers enjoyed the majority of possession in the first-half and Hearts, despite having a physical presence throughout their starting eleven, failed to trouble McGregor up until the interval.
For all the endeavour from the Light Blues in the opening period it looked likely the teams would go in at the break with the scoreline goalless but some excellent play from Bougherra and Lafferty broke the deadlock on 37 minutes.
The Algerian defender picked up the ball on the right-wing after going up for a free-kick and showed terrific pace and skill to beat Jambos’ left-back Lee Wallace.
His drilled cut-back was missed by Lee McCulloch but Lafferty was there to swerve a delightful finish into the back of the net from 18 yards.
The Northern Ireland international celebrated his first Rangers goal in style, skidding along Ibrox’s new turf on his knees in front of a jubilant Main Stand.
Neither side made any changes for the start for a second period which started in a quick-fire manner.
With only a minute gone Mendes fed a delightful ball through to the on-rushing Boyd but his effort on the run was stopped by McDonald who had darted off his goal line.
In the next attack Andrew Driver found was found in acres of space on the left wing and his cross was parried by McGregor.
The ball fell to Ksanavicius but his powerful effort was straight at the grounded Gers keeper who clutched it knowing his luck was in on this occasion.
Smith was to make two attacking substitutions in the 59th and 62nd minute with Kenny Miller and DaMarcus Beasley replacing McCulloch and Lafferty.
And the move almost paid dividends moments later when Beasley used his pace to burst into the penalty box and round McDonald but his cross missed both Velicka and Boyd with the goal gaping.
The game swung in Rangers favour on the 73 minutes when Mikoliunas was sent off for a poor challenge on Kenny Miller after receiving a first yellow card for diving.
The Lithuanian had only been on the pitch for eight minutes.
Rangers continued to push forward in search of a second goal which would have calmed any nerves in the latter stages and it finally came in the 90th minute.
Miller showed his quality with a positive run into the Hearts 18-yard box and Wallace brought the Scotland star down just as he was poised to shoot.
Stuart Dougall immediately pointed to the spot and Boyd did not hesitate in slamming the ball low to McDonald’s right.
Overall, this display was another sign that Rangers are moving gradually in the right direction and the introduction of Mendes was just what the doctor ordered.