Nasri's season has been ravaged by a thigh tendon injury that required surgery and his resulting absence from City's UEFA Champions League squad means he will not feature in the concluding leg of the quarter-final versus Paris Saint-Germain on Wednesday.
Manuel Pellegrini made five changes to his side with an eye on that tie and City subsequently lacked fluency against a West Brom team apparently liberated by reaching the feted 40-point mark last weekend.
Sergio Aguero cancelled out Stephane Sessegnon's early opener in the 19th minute but West Brom carried a threat that a creaking City rearguard rarely contained with any comfort.
Pellegrini was forced to send on reinforcements in the form of Yaya Toure and Kevin De Bruyne and their introduction cranked a lacklustre performance through the gears long enough for Nasri to settle matters.
City are four points ahead of Manchester United in fifth, their rivals travel to title-chasing Tottenham, and two behind Arsenal in third after recording back-to-back Premier League wins for the first time since October.
Great result really difficult game but we did what was needed . Can't express how it feels to be… https://t.co/boyPBSUbUa— Samir Nasri Official (@SamNasri19) April 9, 2016
James McClean and Sessegnon returned to the West Brom line-up and repaid Pulis' faith in the fifth minute.
McClean scampered down the left and his deep cross found Sessegnon at the edge of the box. Aleksandar Kolarov was slow to close down and the winger fizzed in a shot at the near post with Joe Hart rooted to the spot.
City did not respond with any particular gusto but Sessegnon went from hero to villain when he untidily brought down Kolarov and Aguero coolly slotted the resulting penalty beyond Ben Foster's dive.
West Brom's setback was compounded by top scorer Salomon Rondon departing through injury, although they continued to ask questions of a City defence performing with a now familiar lack of conviction in the absence captain Vincent Kompany.
Rondon's replacement, Craig Gardner, fired wide on the edge of the box from Saido Berahino's deft lay-off and slammed a 33rd-minute free-kick into a heavily manned City wall.
By comparison, Aguero ploughed a lone furrow in attack and the interval was welcome for the hosts.
The Argentina international continued to dazzle on his 200th City appearance and Foster did well to push a rasping drive out of the bottom left corner in the 55th minute.
Having scored in both of his appearances since returning from knee ligament damage, De Bruyne again made his presence felt as City took the lead in the 66th minute.
The Belgium international tore down the right and released Jesus Navas into the area and, although Aguero was twice thwarted by last-ditch challenges in his attempts to convert, Nasri was on hand to nutmeg James Chester on the line.
Berahino spurned a glorious chance to level with 16 minutes remaining, when the linesman's flag incorrectly stayed down but he sidefooted wide from close range.
City's afternoon concluded with the unwelcome sight of Aguero limping off following a number of heavy challenges, although relief was palpable at the Etihad when McClean's stoppage-time drive flew through a crowded penalty area and agonisingly wide.
