Scotland enjoyed the lion's share of possession in the opening stages and controlled play with patience against a stubborn Cyprus defence.
However, the visitors struggled to contain Premier League duo Andrew Roberson and Stuart Armstrong on the left flank, and the former proved instrumental in forging the Scots’ first major chance, delivering well to John McGinn, only for the Aston Villa captain to fire off target.
Aaron Hickey then came close for Scotland after he weaved past a number of Cyprus players before getting a shot away, but Cyprus goalkeeper Demetris Demitriou got down well to thwart him as the Hampden Park faithful sensed blood.
Shortly after Demitriou’s opposite number Angus Gunn comfortably saved Grigoris Kastanos’ attempt on goal with his first real action of the afternoon, Robertson and McGinn struck gold at the second time of asking, with the latter firing home at the back post from the Liverpool man’s delivery.
A VAR review ensued for a potential offside against Robertson, but McGinn’s 16th goal for the Tartan Army in 53 appearances would stand.
Now visibly full of fire, Scotland had a chance to double their lead just before the break when McGinn pulled the ball back for Che Adams to strike, but Demitriou pulled off a great save and tipped the ball over the bar.
The hosts then continued to press Group A’s lowest-seeded side after a scrappy start to the second half.
The killer blow nearly came when Hickey and McGinn combined well, but the latter’s effort caused a Mexican wave of groans to echo around Hampden Park.
A tense final 20 minutes ensued, but a second goal eventually came through Scott McTominay, who finished off a well worked move that saw Ryan Christie dispossess a Cyprus defender before picking out QPR forward Lyndon Dykes.
He cushioned a header in the box for McTominay to volley home, and the Manchester United man would also score a second deep into injury-time, when McGinn found Christie who found Robertson with his cut-back.
The Liverpool defender subsequently picked out McTominay, who easily placed the ball past Demetriou for number three.
While Scotland had little trouble in dispatching a weak Cyprus side, who are yet to play in any major tournament, the Tartan Army know that they simply have to be more clinical when facing the sterner tests in Group A of these Euro qualifiers.
Their next opponents Spain will surely punish them in midweek if the Scots prove to be as profligate as they were before the break – though a raucous Hampden Park under the lights can only intimidate ‘La Roja’, against whom Scotland last won back in November 1984.
Flashscore Man of the Match: John McGinn (Scotland)