Recalled to the squad by manager Luc Holtz, Rodrigues made an instant impact after being introduced at half-time, finding the net with a swivelling 25-yard effort.
The Red Lions had been thoroughly outplayed in the first half by a spirited Iceland side, with new Lille signing Hakon Haraldsson proving a particular threat on the left wing.
The visitors started slowly in freezing conditions in Reykjavik, Luxembourg goalkeeper Anthony Moris making a fine save to deny Haraldsson early on, before the home side saw a shot deflected onto the bar.
The pressure finally began to tell and it was FC Copenhagen forward Orri Oskarsson who put Iceland in front with a tap-in halfway after 22 minutes.
The Red Lions were fortunate to go into half-time only a single goal down, but the match turned on its head with Rodrigues’s brilliant effort just after the break.
The simultaneous introduction of veteran right-back Laurent Jans helped to neutralise Haraldsson and spurred the visitors on to a much-improved second-half performance.
Iceland saw former captain Gylfi Sigurdsson make a first appearance in two years after child sexual offence charges against him were dropped, but was unable to make the difference as Luxembourg pressed for victory.
St Pauli forward Danel Sinani hit the crossbar with a fine curling effort from distance, and the away side had an even better chance to win it in extra-time.
With Iceland needing a win to have any chance of qualification for Euro 2024, Arsenal goalkeeper Runar Runarsson made his way up for a last-gasp corner but was caught out of position as the ball was cleared straight to Gerson Rodrigues.
The former Metz man almost secured an incredible three points for the Red Lions, but couldn’t convert an open goal from about 40 yards under pressure from a defender.
The result leaves Luxembourg third in Group J, just two points behind second-placed Slovakia ahead of the two sides’ meeting in the Grand Duchy on Monday.
