Miller fired home a stunning lob midway through the first half after a shaky start from the visitors.
Mackie brilliantly cut inside his marker before sliding home the second in the 56th minute but Dimitris Christofi soon pulled one back.
The goals were significantly more impressive than Scotland’s overall performance, with Cyprus twice hitting the post before the visitors finished the first half strongly.
Scotland’s victory – their seventh in 11 internationals – was never in doubt but the close nature of the final half-hour prevented manager Craig Levein experimenting with two up front until the final four minutes when he handed Jordan Rhodes a brief debut.
But the night belonged to Miller and Mackie for their two superbly-taken goals.
Miller instantly controlled Christophe Berra’s long diagonal ball over the top and lobbed the ball over the home goalkeeper and into the far top corner from 18 yards.
The goal, Miller’s 16th for his country, took him to sixth place in Scotland’s all-time goalscorer’s list ahead of James McFadden.
Only Denis Law, Kenny Dalglish, Hughie Gallacher, Lawrie Reilly and Ally McCoist have scored more than the 31-year-old, who was winning his 58th cap.
Mackie netted his second goal in four internationals – the last of each coming a year ago against the Faroe Islands before he broke his leg in January.
The QPR player, making his sixth appearance since his comeback, cut in from his position on the left flank and turned his man brilliantly before a composed finish.
Cyprus coach Nikos Nioplias left out a number of established players from his squad following a disappointing Euro 2012 campaign that saw them pick up just two points, but all of his starting line-up had some previous international experience.
The Scotland players lined up for the national anthem with poppies on their tracksuits and started with black armbands with the symbol embroidered.
The Scottish Football Association had followed the lead of their English counterparts following negotiations with FIFA over the Armistice Day tribute but most of the armbands fell off in the opening stages.
Darren Fletcher started in the anchor role with Scotland’s other four midfielders taking up advanced positions but it was the home side who got two decent early efforts on target.
Allan McGregor comfortably saved from Georgios Efrem’s angled shot and a header from Christofi but the space afforded to the home side would have concerned Levein.
Israeli referee Meir Levy, who took charge of a Hamilton versus St Mirren game a year ago amid a strike by Scottish referees, booked home full-back Jason Demetriou for a foul on Mackie before Scotland had their first close escape.
Efrem, who failed to make the Rangers first team during a two-year spell at Ibrox, turned inside Berra on the edge of the box after a long ball and fired a volley that McGregor tipped on to the crossbar.
Miller pulled a left-footed shot wide from Barry Robson’s crossfield ball before a perfect second attempt in the 23rd minute to delight around 500 Scotland fans behind the goal, who outnumbered the home fans by around 10 to one.
Cyprus struck the woodwork again three minutes later when Sinisa Dobrasinovic fired a 25-yard strike off the inside of the post.
But Scotland began to assert more control and Mackie almost added another memorable goal when he drove down the left in between two men and evaded another inside the box before firing a left-foot shot that was pushed over the bar by Antonis Giorgallidis.
Berra and Phil Bardsley each headed just wide and Miller almost claimed his second after James Morrison had released Steven Whittaker down the right.
The full-back hit the byline before his low delivery took out the goalkeeper but the grounded Miller could not turn it home after sliding in with a home defender and the ball bounced wide off Robson.
Giorgallidis pushed over Morrison’s chip shot as Scotland finished the half on top.
Scotland controlled possession in the opening stages of the second half and Robson thumped a powerful 20-yard strike following a short corner that substitute goalkeeper Tasos Kissas stopped.
Gary Caldwell blocked well from Dobranisovic after Scotland had been cut open on the left side of their defence but Mackie soon doubled their lead.
Robson and Mackie worked space on the left and the QPR player turned his man one way and the other in the box before placing the ball inside the far post with his right foot.
Cyprus hit back three minutes later when left-back Bardsley was caught out with a pass inside him and Christofi fired into the far corner.
Levein made a double switch in the 64th minute with Craig Mackail-Smith and James McArthur coming on for Miller and Fletcher.
Stephen Crainey came on for Bardsley, who had missed several days’ training and had to rearrange strapping on his ankle in the opening stages.
McGregor caught a powerful long-range effort from Antonis Katsis but neither side could break away in the final quarter with Craig Conway handed the final 10 minutes in place of Robson.
Huddersfield striker Rhodes replaced Mackie in the 87th minute and played up front alongside Mackail-Smith, who saw his follow-up diverted wide after an injury-time break and shot from Morrison.