Borussia Moenchengladbach needed a 90th-minute equaliser from World Cup winner Christoph Kramer to draw 1-1 with VfB Stuttgart in Sunday's other match.
Despite a squad budget of around five million euros ($6.62 million)- the smallest in the league - minnows Paderborn refused to buckle against their more experienced rivals, rewarding their 14,000 fans with their first point in their maiden top-flight appearance.
"I am very satisfied with our performance," said Paderborn coach Andre Breitenreiter. "They ran, they fought and had courage. We would have deserved to have left the pitch as winners and we can all be very proud.
"We could have had a bit better possession in stoppage time but we can build on this performance today," he said.
Japan striker Shinji Okazaki fired Mainz into the lead after tapping in from five metres following a free kick.
North Rhine-Westphalian club Paderborn, who finished a surprise second in the second division last season, kept their cool and earned an equaliser with Elias Kachunga's powerful drive from 17 metres.
Uwe Huenemeier's header three minutes from time from a Marvin Bakalorz cross triggered wild celebrations as the hosts thought they had sealed a memorable first win.
But Mainz kept at it, Okazaki rattling the post with a header in the last minute of regular time as they dug deep to avoid a season-opening defeat.
They were awarded a penalty in stoppage time after Huenemeier went from hero to villain in just a few minutes, bringing down Okazaki. Koo Ja-cheol converted the spot kick to save Mainz's blushes.
In Moenchengladbach, Kramer rescued a 1-1 draw with his 90th-minute equaliser after Alexandru Maxim had profited from a deflection and a fine pass from Christian Gentner to give Stuttgart the lead early in the second half.
New arrival Thorgan Hazard, brother of Belgium winger Eden, pumped some life into Gladbach's game when he hit the post minutes after coming on in the second half and Branimir Hrgota missed a simple tap-in.
But it was fellow substitute Kramer, who had come on in the 74th minute, who snatched the last-gasp equaliser and a point for the hosts with a low drive from inside the box to spoil coach Armin Veh's return to the Stuttgart bench.
Champions Bayern Munich got off to a winning start on Friday, beating VfL Wolfsburg 2-1, while last season's runners-up Borussia Dortmund slumped to a 2-0 home defeat against Bayer Leverkusen on Saturday.
(Reporting by Karolos Grohmann; editing by Josh Reich)
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