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 UEFA 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 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 Round of 16 exit.
City may have held a huge first-leg lead but it wasted no time in extending it, opening the scoring in the eighth minute.
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 UEFA 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 UEFA 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 coach's third European title.