Midfielder Gylfi Sigurdsson rescued a point to keep the Londoners in touch with Group J leaders Lazio, who could only manage the same scoreline at Panathinaikos.
Spurs trail the Italians by two points after a poor showing at the Stadion Ljudski, where last season Maribor were not good enough to see off second tier English Championship side Birmingham.
Robert Beric fired in from close range three minutes before the break for Maribor but Spurs' boss Andre Villas-Boas sent on Spaniard Iago Falque and he whipped over the cross which ultimately saw Sigurdsson convert in a goalmouth melee.
Beaten at home by Chelsea at the weekend, Spurs had every reason to atone with Villas-Boas making three changes as Hugo Lloris, Kyle Naughton and Andros Townsend came in.
But they could not prise apart a dogged home side despite early pressure and Ales Mejac could have inflicted further damage as he fired just off target shortly before Beric bundled in the hosts' goal.
Of some consolation to Spurs was Jose Verdu Nicolas's last-gasp leveller for Panathinaikos which denied Lazio a win which looked to be there for the taking for the Romans after Georgios Seitaridis had put through his own goal in the first half.
In other early action, Genk of Belgium made it three wins in three by defeating Sporting Lisbon 2-1 while Hungary's Videoton are second after beating Swiss side Basel in Group G.
Former European champions Inter Milan lead Group H after Rodrigo Palacio netted the only goal against Partizan Belgrade but Russia's Rubin Kazan edged Neftci of Azerbaijan by the same score to stay level on points with seven from three games.
French side Lyon thanked a Jimmy Briand goal four minutes from time for a third straight success -- 2-1 over Group I tailenders Athletic Bilbao and Sparta Prague lie second after a 3-1 win over Israel's Hapoel Kiryat Shmona.
Five-time European champions Liverpool were later hoping to avoid a second straight home reverse in Europe for the first time in their history when they took on big-spending Russian outfit Anzhi Makhachkala at Anfield having already lost to Udinese on Merseyside.
Anzhi, thanks to the financial backing from wealthy owner Suleyman Kerimov, have started to flex their muscles this season with Guus Hiddink guiding the Dagestan-based club to the top of the Russian Premier League.
Anzhi and Udinese -- facing Swiss makeweights Young Boys -- currently lead the Reds by a point.
Newcastle were another English side in action, the Group D leaders welcoming Club Brugge of Belgium to St James' Park on Thursday while rivals Bordeaux were at Portugal's Maritimo.
Source: AFP
Source: AFP