One of the stand-out performers in his country's surprise run to the semi-finals of Euro 2016, Ramsey was making his first start of the current campaign following persistent fitness problems.
But the Juventus midfielder re-announced himself in style at a fervent Cardiff City Stadium, scoring a goal in each half as Wales deservedly claimed the win they needed to leapfrog Hungary and take the second automatic qualifying spot in Group E.
Gareth Bale, Daniel James and the goalscorer buzzed effectively behind imposing targetman Kieffer Moore throughout, although Giggs was also indebted to some first-half heroics from goalkeeper Wayne Hennessey.
Wales began confidently and, when Adam Lang made the mistake of showing Bale on to his left foot on the right flank, the Real Madrid star whipped in an inviting cross for Ramsey to gleefully nod home.
Another wonderful Bale delivery – this time right-footed – saw Moore head narrowly wide in the 29th minute.
Hennessey produced a remarkable double-save to thwart Dominik Szoboszlai and Roland Sallai at close quarters in the 34th minute and it would prove a pivotal moment.
Instead of chasing the game, Wales were able to resume in composed fashion after the break and they soon had breathing space.
Moore – a handful in the air throughout for the Hungary defence - knocked down Ben Davies' 47th-minute set-piece and Ramsey, left negligently unmarked for a man of his finishing capabilities, made no mistake.
Giggs' eye-catching attacking midfield trio started to run through their repertoire, with Bale fizzing a free-kick narrowly over before James cut in to curl a shot just beyond the top-right corner.
An awful challenge from Istvan Kovacs on fellow substitute Ethan Ampadu highlighted Hungary's simmering frustration, while Peter Gulacsi saved with his boot to deny Ramsey the match ball 15 minutes from time.
What does it mean? Back-to-back Euros for Wales
Although UEFA's expansion to a 24-team tournament has leant a helping hand, Wales' achievement in reaching consecutive European Championships is a significant one for a country whose previous major tournament was the 1958 World Cup. Giggs has remained committed to letting promising youthful players flourish alongside his established stars, despite a rocky start in the group, and deserves his share of credit.
Rambo draws first and last blood
Wales got themselves in position without Ramsey but there is no doubt they go up a level with the former Arsenal man in their line-up. Fitness permitting, no nation will relish facing Bale, James and Ramsey in tandem come June.
Lang error costly for Hungary
That said, there are better ways to combat Bale than ushering him on to his lethal left foot to set up the opener. Hungary's night might still have been one of savour but for Lang's lapse.
Key Opta Facts
- Wales have won back-to-back competitive games for the first time under Giggs, having last done so in October 2017 under Chris Coleman.
- Hungary have now lost six of their last seven away games in major tournament qualification (World Cup and European Championships), failing to score in five of those.
- Ramsey netted his first brace for Wales in his 60th appearance for his national side.
- Wales' opener was the first time Bale had set up a goal for Ramsey since March 2015 against Israel, four years and 236 days ago.
- Bale has been directly involved in 12 goals in his last 11 competitive home games for Wales, scoring nine and assisting three.
Hungary get another bite at qualification in March's play-offs – the dream of turning out in the finals at Budapest's Puskas Arena still alive. Bale and his team-mates can dream of another unlikely tilt at European glory.