It was one-way traffic before the goal eventually arrived, with Griffiths failing to make contact from close range and James McArthur seeing the follow-up attempt blocked in front of goal after keeper Andrew Hogg fluffed his lines from a cross.
A towering header from Berra opened the scoring for the Scots nine minutes in, climbing above his man to get the ball over the line from one of a number of first-half openings for the centre-back.
Chances then came and went for James Forrest and Armstrong, the former of whom forced a decent stop out of Hogg, while Matt Phillips's shot dipped in front of the visiting keeper to give him something to think about.
For all Scotland's dominance they could not make their possession truly count, however, as Malta - now without a win in 22 competitive outings and ranked a lowly 190 in the FIFA rankings - held out for the interval with just the one goal in it.
It took just four minutes of the second half for the Tartan Army to celebrate a second goal, as Griffiths was given the task of rolling the ball a few inches over the line after half-time sub James Morrison struck the post from slightly further back.
Forrest tested Hogg soon after with a shot towards the bottom corner, before Griffiths picked out the Hibernian stopper down low when played through on goal.
Scotland lacked the quality required in the final third to find another goal, and there was almost a consolation for the visitors - without a goal in nine previous trips to Britain and Ireland - in the final 15 minutes.
Scotland play host to Slovakia in a pivotal fixture here in a month's time, before rounding things off away to Slovenia a few days later - two wins from two being enough to see them finish in second.