The denominational secondary, which serves some of the most deprived communities in the city, has been awarded five "excellent" ratings for personal and social development; expectations and promoting achievement; partnership with parents, the school board and the community; leadership; and self-evaluation.
Of the other 14 quality indicators at the 1,549-pupil school, 12 were rated "very good" and two "good". No aspects were deemed to be "adequate", "weak"
This means that St Andrew's, which has been led by headteacher Bruce Malone for the past 15 years, has effectively set a benchmark for other secondaries under the new HMIE regime.
It will also give the city council some satisfaction that St Andrew's has higher gradings than some of Glasgow's independent schools. Hutcheson's Grammar last week received one "excellent" grading, 12 "very goods", 11 "goods", two "adequates" and one "weak" for its primary and secondary schools; The High School of Glasgow received four "excellent", 10 "very goods", six "goods" and two "adequates".
John Ogilvie High in Hamilton, another state denominational secondary, received two "excellents", nine "very goods", four "goods" and four "adequates".
Steven Purcell, the council's leader, said: "This wonderful report just shows what can be achieved in a school in a socially and economically deprived area. The standards being reached at St Andrew's surpass those not only of schools in similar areas across the country, but also those of schools in many more affluent areas.
"The tremendous work being done by Mr Malone and his team is ensuring that St Andrew's Secondary pupils are being given every chance to fulfil their potential, whatever their background. That's what we want for every youngster in the city."
Inspectors said that one of the key strengths at St Andrew's was the school's outstanding partnerships with parents, community and local parishes.
The report praised teachers for working hard, planning well, sharing the aims of the lessons effectively with pupils, explaining new work clearly and making good use of resources, including ICT, to enliven lessons.
"They regularly set homework which supported class work well," the report stated. "Teachers valued pupils' contributions and praised their efforts.
Pupils responded very positively to the stimulating, learning environment and the high expectations placed upon them. They were attentive, invariably on task and well behaved."
Overall the school's exams performance was much better than similar schools. Leavers were consistently successful in securing employment and training, and increasing numbers went on to further and higher education.
The school's extra-curricular achievements included sustained success in debating and public speaking, with teams twice taking first prize in the prestigious Glasgow Bar Association debating competition; success in the Young Sports Journalist of the Year competition; and a second-year creative writing club which gained a bronze award in the Bridgeton Burns competition.
The combined effect of various pastoral care approaches had had "an outstanding impact on pupils' personal development".
Mr Malone's leadership was said to be "excellent". He provided "a very strong lead and had very high expectations for all within the school community".
Inspectors said: "He had a clear strategic vision for the school, established effective policies and procedures, and empowered senior and middle managers. The quality of pupils' learning experiences was at the forefront of this vision."
The report also found, however, that "while most staff were highly motivated, the morale of a small number of staff was low as they felt uncomfortable about the very high expectations placed upon them by the headteacher".
It added: "The headteacher and staff had exceptionally high expectations for pupils' behaviour, achievement and attendance. Pupils responded positively to these very high standards. They were commendably well-behaved and co-operative and wore the school uniform with pride."