Earlier on the Bundesliga's first day back following the coronavirus-enforced hiatus, Julian Nagelsmann's Leipzig were held to a 1-1 draw by Freiburg - and Gladbach took full advantage, looking every bit Champions League hopefuls.
The hosts failed to even keep Gladbach at bay for a full minute as Plea put the visitors in front, while Thuram – a key player before the suspension in proceedings – knocked in his seventh in the league this season soon after.
Substitute Andre Silva pulled one back for the hosts late one, but Ramy Bensebaini had already effectively secured a comfortable win for Marco Rose's side with a penalty.
Frankfurt had suffered three successive Bundesliga defeats prior to the break, and within 34 seconds of kick-off that run looked destined to continue – Plea finding the bottom-left corner despite being unbalanced after a one-two with Jonas Hofmann.
It was 2-0 just six minutes later as Bensebaini turned cleverly in the box and squeezed the ball across the face of goal for Thuram to tap in.
Filip Kostic appeared the Frankfurt player most likely to instigate a revival, but his wicked 24th-minute free-kick was pushed away by Yann Sommer, whose only other first-half save kept out Almamy Toure's tame effort from a tight angle just before the interval.
Adi Hutter introduced Silva for the ineffective Djibril Sow at half-time and Frankfurt had a little more presence in attack as a result, though not to the extent that Gladbach's lead ever looked under threat.
The visitors added a third through the lively Bensebaini, who converted from the spot after Breel Embolo was barged over by Evan Ndicka.
Silva grabbed a well-taken consolation with nine minutes to go, though it failed to inspire a comeback.
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After getting their early lead, Gladbach never looked like dropping points here. Once they were two up, they were smart enough to become more compact while still offering a threat on the break.
Frankfurt, on the other hand, showed little creative ingenuity, their forays forward rarely causing undue worry to the Gladbach defence. Defeat means they remain just five points above the bottom three.
Double trouble for Gladbach
Thuram and Plea were both effective, getting a goal apiece. The latter arguably shaded his younger compatriot, who appeared to suffer a knock in the second half, as the ex-Nice forward also hit the post while seeing a late opportunity saved.
Sow nowhere to be seen
An anonymous first-half showing resulted in Sow's withdrawal at the break in favor of the more attack-minded Silva.
Gladbach return home – where they will play in front of approximately 12,000 cardboard cut-outs instead of fans – next weekend, with Bayer Leverkusen the visitors. Life will not get any easier for Frankfurt in a week, however, as they go to Bayern Munich.