The newly crowned Women's Super League champions took the lead when Fran Kirby skipped past her marker and hit a sweet strike from the edge of the area.
The visitors' best chance fell to Kelly Montgomery just after the break, but she volleyed over the bar.
Glasgow keeper Lee Alexander also saved well from Millie Bright and Ana Borges.
England striker Kirby had netted twice in the 4-0 win over Sunderland that sealed Chelsea's first league title on Sunday, and proved to be their matchwinner again with her 39th-minute effort.
Glasgow, who reached the quarter-finals of the competition last season, struggled to create chances but were left to rue Montgomery's miss.
The lively Kirby shot wide after escaping from a crowd of defenders as Chelsea pushed for a second, and after denying Bright and substitute Borges, Alexander did well late on to hold another rising strike from Kirby, giving the Scottish league champions hope for next Wednesday's second leg in Glasgow.
Chelsea Ladies boss Emma Hayes told BBC Sport:
"To win 1-0 at home with a clean sheet, for the first time (in Europe) in Chelsea's history, we have to savour these moments.
"Overall it was a good performance.
"If it wasn't for their goalkeeper, we'd be talking about at least a two-goal lead tonight."
Glasgow City boss Scott Booth told BBC Sport:
"I thought we were excellent. We came here to do a certain job and I couldn't have asked any more of my players.
"We came up against some of the best players in the world. We more than matched them at times.
"We were undone by a moment of brilliance from Kirby. I'm looking forward to the away leg, because we're still in this."
Chelsea Ladies: Lindahl, Blundell, Bright, Flaherty (c), Fahey, Davison, Aluko (Borges 68), Ji, Rafferty, Kirby, Spence (Coombs 80)
Subs not used: Hourihan, Chapman, Brett, Meiwald, Ayane
Glasgow City: Alexander, Lauder, Love (Rafferty 88), O'Sullivan, Montgomery, Docherty, McCulloch, Ross (c), Grant, Corsie, Cuthbert (Shine 72)
Subs not used: Cunningham, McMurchie, Jones, Shine, Whyte, Fleeting
Referee: Olga Zadinova
Attendance: 1,100

The charity said the new technology would provide an alternative to road ambulance journeys, offering significantly quicker transport of vulnerable babies between hospitals.
The service began carrying Babypods for emergency missions in 2013.
But the new incubators will attach to existing equipment in the helicopter, providing warmth and oxygen.
They also have a transparent chamber, allowing babies to be monitored during flights.
Welsh medics went to Switzerland to help in the design process and, at a cost of Â£70,000 each, two new incubators have been bought by NHS Wales.
They will be used on Wales Air Ambulance's newest helicopter, the fourth in its fleet.
Weighing 15st 10lb (100kg), the incubators will be fitted to a sled and require two people to lift them into the air ambulance.
Since April 2015, helicopter crews have been joined on board by consultant doctors.
Dr Dindi Gill, the Emergency Medical Retrieval and Transfer Service Cymru interim director, said: "Having the incubator system will further enhance the ability of the EMRTS teams to manage neonates born at home or in hospital.
"It is recognised that temperature control is extremely important to this group of patients and, therefore, we welcome the ability to carry the incubator on Wales Air Ambulance's helicopters."
Following crew training, the incubator service will run as a trial to the end of 2016.
Chelsea Ladies will take a slender lead into the second leg of their Champions League last 32 tie with Glasgow City after winning on their European debut.
[NEXT_CONCEPT]
The most advanced flight incubators in the UK for sick babies will be used by Wales Air Ambulance later this month.