The visitors defeated newly promoted SV Darmstadt 98 as expected, with Randal Kolo Muani's goal the difference between the two sides.
Match preview
Mainz, on the other hand, saw their season get off to a disastrous start when thrashed by Union Berlin on Sunday, with Kevin Behrens firing in two goals inside the opening 10 minutes of the encounter.
The 32-year-old striker later completed his hat-trick after Anthony Caci had provided some hope of the visitors pulling off a comeback, with Milos Pantovic putting any miniscule possibility of that to bed by adding further gloss to Urs Fischer's side's victory deep into injury time.
Having finished in the top half in both of Bo Svensson's full seasons in charge of Die Nullfunfer - albeit narrowly missing out on qualifying for Europe on both occasions - Mainz will be hoping to at least replicate that achievement this time around.
However, with all bar one of the teams which finished above them at the end of last season's table spending more money than them so far this transfer window, that may prove to be difficult for Svensson's side. All they can do is take one game at a time and hope to build some momentum through at least one period during the campaign.
Frankfurt, on the other hand, will have expectations of challenging for the Champions League qualification positions having appeared in Europe's elite competition for the first time in their history last season.
Dino Toppmoller has replaced Oliver Glasner in Die Adler's managerial dugout, having previously worked as Julian Nagelsmann's assistant manager at RB Leipzig and Bayern Munich, and he got off to a decent start by edging past Darmstadt on Sunday.
Kolo Muani - who has been linked with a move to Paris Saint-Germain in recent days - scored the only goal of the game five minutes before half-time, with Toppmoller's side unable to find a second goal despite enjoying 62% of possession against their newly promoted opponent.
After drawing 1-1 away to Levski Sofia in the first leg of their Europa Conference League qualifying tie on Thursday evening, Frankfurt will be aiming to add to their European trophy cabinet following their unexpected Europa League triumph 15 months ago, while targeting maximum points in the Bundesliga ahead of September's international break.
Mainz 05 Bundesliga form:
L
L
L
L
D
L
Mainz 05 form (all competitions):
L
L
D
W
W
L
Eintracht Frankfurt Bundesliga form:
D
L
W
D
W
W
Eintracht Frankfurt form (all competitions):
D
W
L
D
W
W
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Team News
Mainz appear likely to remain without Andreas Hanche-Olsen, Silvan Widmer and Jonathan Burkardt due to injury, with the trio expected to remain out of action until after the international break.
Svensson may be tempted to ring the changes given their poor performance in the capital on the opening weekend, with Tom Krauss and Sepp van den Berg providing two options to mix things up after making their league debuts from the bench.
Frankfurt, meanwhile, will remain without Paxten Aaronson, Mehdi Loune and Lucas Alario due to injury, while club captain Sebastian Rode has been ruled out for almost a month after sustaining a calf injury against Darmstadt.
Hugo Larsson and Makoto Hasebe are both doubts due to illness, but Kristijan Jakic should be fit enough to replace Rode from the start in the visitors' engine room.
Mainz 05 possible starting lineup:
Zentner; Van den Berg, Bell, Fernandes; Da Costa, Barreiro, Krauss, Caci; Onisiwo, Lee; Ajorque
Eintracht Frankfurt possible starting lineup:
Trapp; Tuta, Koch, Pacho; Ebimbe, Skhiri, Jakic, Max; Gotze, Kolo Muani, Lindstrom
We say: Mainz 05 1-1 Eintracht Frankfurt
Mainz were far from their best when being soundly beaten by Union Berlin last weekend, and we can envisage Frankfurt smelling a bit of blood on Sunday.
They do have a disadvantage having played in Europe on Thursday evening, though, which could help the hosts attain a share of the spoils at least.