A comprehensive 4-0 win in Switzerland three weeks ago gave City a foot in the last eight and the chance of a Basel comeback was always extremely remote, but the hosts struggled for cohesion after nine changes and slipped to a first home defeat in any competition since December 2016.
Guardiola took the chance to rest stars including Kevin De Bruyne, Sergio Aguero, Ederson and David Silva, with Phil Foden starting to become the youngest English player to start a knockout game in the Champions League.
Teenager Foden featured alongside Yaya Toure - 17 years his senior - in midfield but the duo struggled to retain control of the contest, although City took an early lead on the night.
Leroy Sane carried the ball past a series of defenders and slipped it through to Bernardo Silva, whose low cross was ideal for Gabriel Jesus to score his first goal since returning from two months out with a knee ligament injury.
Basel came from behind to win at the Etihad Stadium, though, Mohamed Elyounoussi slamming a finish past reserve goalkeeper Claudio Bravo and then setting up Michael Lang for a fine strike to send the visiting supporters home happy despite their team's last-16 exit.
City may have held a huge first-leg lead but they wasted no time in extending it, opening the scoring in the eighth minute.
13 - Gabriel Jesus has scored his first goal for Manchester City since November 18th 2017, ending a 13-game run without a goal for the club. Satisfaction.— OptaJoe (@OptaJoe) March 7, 2018
Sane's driving run created space on the right for Silva, whose low cross provided Jesus with a tap-in for his first goal since November.
Basel keeper Tomas Vaclik did well to deny Ilkay Gundogan and Basel immediately broke and equalised.
A Blas Riveros shot deflected straight to Elyounoussi, who thumped home into Bravo's bottom-right corner.
Dimitri Oberlin scored in each of his previous two Champions League away games and the forward almost extended that run, curling a free-kick into the side netting.
Basel continued to work openings but Riveros fired straight at Bravo in the 39th minute.
With both sides struggling for penetration after the restart, Guardiola sent on another of City's talented youngsters, Brahim Diaz, in the hope of sparking life into the contest.
But it was Basel who nudged ahead with 19 minutes to go. Jesus lost possession on the halfway line and Elyounoussi led the sluggish Toure on a merry dance down the right wing before slotting Lang through on goal, the right-back beating Bravo with a powerful finish from a tight angle.
Diaz hammered a drive straight at Vaclik in the 79th minute as City tried to battle back, but Basel held firm to earn a memorable victory.
City's passage into the quarter-finals was never in doubt but a second Champions League defeat of the season – Guardiola's men lost a dead rubber at Shakhtar Donetsk in the group stage – may raise questions about their chances of claiming the Catalan's third European title.
Key Opta facts:
- Manchester City have made it through to the quarter-finals of the Champions League for just the second time in the club's history, having only previously done so in 2015-16 when they reached the semi-finals (knocked out by Real Madrid).
- However, Basel's 2-1 victory this evening has ended Manchester City's 13-game winning streak at home as well as their 36-game unbeaten run at the Etihad Stadium in all competitions (W29 D7) - their first defeat on home soil since the December 3, 2016, losing 3-1 against Chelsea in the Premier League.
- Manchester City have never won the second leg of a last 16 tie in the Champions League (W0 D1 L4).
- Only Barcelona (23), Bayern Munich (15), Real Madrid (11) and Juventus (9) have won more Champions League games against English clubs than Basel (6).
- Manchester City completed 978 passes in this game – the most recorded by a side in a Champions League match since 2003-04 (when Opta began recording this metric).