The Cappielow men set up in a 4-3-3 formation - which, in the event, more resembled a 4-5-1 such was the opposition's early dominance - with a starting XI that included six trialists.
In defence, summer signing Willie Dyer was joined by recently released Hibs youngster Scott Taggart at right-back, ex-Hamilton man Simon Mensing and a Spanish centre-half known as Polako.
Former Motherwell midfielder Ross Forbes played alongside Kyle Wilkie and experienced campaigner Martin Hardie in the middle of the park
Tony Wallace, who Ton boss Allan Moore hopes to tie up on a deal later today, and David O'Brien lined up on the flanks while Peter Weatherson acted as a focal point for the attack.
For their part, Rapid, who finished fourth in Liga 1 to qualify for the Europa League, named a squad replete with international players, with no fewer than seven of the starting line-up having won caps at senior level.
Furthermore, the Romanian giants already have three pre-season friendlies under their belt, and those extra weeks of training were evident as they raced into an early two-goal lead.
In the eighth minute, attacking midfielder Stefan Grigorie placed a low shot past Derek Gaston to open the scoring.
Then, three minutes later, Mihai Roman tapped home from six yards after a Nemanja Milisavljevic cross from the left found him lurking at the far post.
Morton were sluggish in the first half hour, and only an inspired showing by impressive new goalkeeper Gaston prevented Rapid from adding to their advantage until the 39th minute.
The 25-year-old former Albion Rovers custodian made four fantastic stops in the first 45 and also impressed in one-on-one situations, twice forcing his opponent wide to an impossible angle.
But he had little chance when slack play in the midfield gifted Rapid a four-on-one counter-attack which ended with Sabrin Sburlea turning Polako inside out before rifling into the bottom right-hand corner.
At the other end, Ton's best effort of the half was a Forbes free kick from 25 yards which finished narrowly wide of the upright.
The interval saw Moore ring the changes as he brought on familiar faces in Michael Tidser and Archie Campbell as well as recent acquisitions Jordan Halsman, David Graham and Stephen Stirling.
The side now had the look of the team that will be likely to take to the field for the first game of the new campaign against Albion Rovers, and it was at this stage that they began to find their feet.
Moore has been effusive in his praise of Gaston's kicking ability - and it was as a consequence of one of his unfeasibly long kick outs that Morton pulled a goal back in the 58th minute.
Peter Weatherson attempted to win the punt in the opposition box but was bundled to the ground and the man in the middle pointed to the spot.
The long-serving striker picked himself up and, showing he had been paying keen attention to the exploits of Andrea Pirlo and Sergio Ramos in the Euro Championship, clipped an audacious 'Panenka' penalty down the middle to reduce the deficit.
However, less than a minute later Rapid were awarded a penalty of their own when Thomas O'Ware was penalised for a crude tackle. Substitute Ovidiu Herea made no mistake, placing the spot-kick beyond Gaston's despairing dive.
Herea added a fifth in the 76th minute by slamming home the rebound after Gaston had flicked out a boot to touch a shot onto the post and make yet another impressive save.
Campbell completed the scoring five minutes from the end when he scooped the ball into the net from close range after the visitors' keeper, Danut Coman, had parried Tidser's powerful drive from the edge of the box.
First Half (4-5-1/4-3-3): Gaston; Taggart [Trialist], Polako [Trialist], Mensing [Trialist], Dyer; Wallace [Trialist], Wilkie [Trialist], Hardie [Trialist], Forbes [Trialist], O'Brien; Weatherson .
Second Half (4-4-2): Gaston; McNeil [Trialist], Polako [Trialist], Mensing [Trialist] (O'Ware, 54), Halsman; Graham, Stirling (Blair, 83), Tidser, O'Brien (Nicholson, 67); Campbell, Weatherson (Hawke, 74).
Coman; Voicu, Abrudan, Oros, Roman, Grigore, Teixeira, Milasavljevic, Grigorie, Pancu, Sburlea.
Subs: Albut, Draghia, Duarte, Burca, Berti, Da Silva, Pavlovic, Surdu, Goga, Herea, Patrascu.
Ton's Star Man: Derek Gaston - The 25-year-old goalkeeper was recently signed from Albion Rovers as back-up to experienced number one Alan Combe.
Despite conceding five goals, he made a string of superb stops to keep the score down and may well claim the keeper's jersey if he continues to perform as he did against Rapid.