Villa remain bottom of the table and five points from safety but did at least end a seven-game losing streak after surviving a late scare when Fernando thumped the bar.
It was a deserved point for Garde while for City, on a day when rivals Arsenal were engaged in a north London derby with Tottenham, it was a case of dropping points.
Brad Guzan’s reaction stop denied Raheem Sterling, and Kevin De Bruyne missed a glorious second-half chance as City failed to find a breakthrough.
With six changes, which included dropping Jack Grealish and Joleon Lescott, Garde stamped his authority on Villa and they reacted well.
There was a renewed sense of confidence despite their run of losses, the first six of which led to former manager Tim Sherwood’s sacking.
Villa were comfortable on the ball without initially threatening and it was City who eventually conjured the first chance.
Aleksandar Kolarov had already flashed a dangerous ball across goal before Guzan almost gifted him a 17th-minute opener.
Sterling bamboozled Alan Hutton to find the overlapping Kolarov and the defender’s tame shot was scooped onto the outside of the post by Guzan.
From the corner Fernando shot over but it was the first sign City were stirring, even if they lost Wilfried Bony to injury after 24 minutes.
Despite their early composure the closest Villa came was Idrissa Gana’s rising drive which flew over Joe Hart’s bar.
Villa, though, matched City with the visitors struggling to find a rhythm and focal point without the injured Bony.
City increasingly relied on Sterling’s pace to stretch their hosts but Villa managed to keep him on a tight leash.
He was City’s best outlet and the England man wanted a penalty eight minutes before half-time when Yaya Toure set him free and he tangled with Ciaran Clark.
It looked soft and summed up City’s first-half attacking play as they laboured without the influence of the injured Sergio Aguero.
Sterling moved to the centre of the visitors’ attack during a reshuffle by Manuel Pellegrini at the break and he should have opened the scoring after 54 minutes.
Jesus Navas teased Villa on the right and produced a fine cross for the unmarked Sterling, who was denied by Guzan’s reflex save.
Replays showed the goalkeeper stopped Sterling’s six-yard header with his face but the England man should not have given the American a hope.
It was a bad miss but worse was to follow when De Bruyne failed to convert Navas’ cross from four yards after 66 minutes.
The midfielder tried to flick the ball in with his heel but only succeeded in scuffing horribly wide.
The visitors were running out of ideas and threw on Fabian Delph against his former club, with the former Villa midfielder mercilessly jeered after his summer switch.
It did little to boost City’s attacking threat but they almost claimed victory in injury time when Fernando’s header hit the bar and Delph fired the rebound wide.