The Minstermen opened the scoring in the ninth minute when Richard Brodie directed his header home from Connolly's corner.
But they had to wait until the 84th minute to double their lead, Connolly drilling an effort into the far corner.
Scott Fenwick added a third in the 89th minute, converting Kaine Felix's cross from the right, and there was still time for Connolly to score his second of the day after rounding the goalkeeper.
Report supplied by the Press Association
Match ends, York City 4, Solihull Moors 0.
Second Half ends, York City 4, Solihull Moors 0.
Goal!  York City 4, Solihull Moors 0. Aidan Connolly (York City).
Goal!  York City 3, Solihull Moors 0. Scott Fenwick (York City).
Substitution, York City. Scott Fenwick replaces Richard Brodie.
Goal!  York City 2, Solihull Moors 0. Aidan Connolly (York City).
Substitution, Solihull Moors. Omari Sterling-James replaces Jordan Fagbola.
Substitution, York City. Kaine Felix replaces Jake Wright.
Substitution, Solihull Moors. Stefan Moore replaces Darryl Knights.
Substitution, Solihull Moors. Harry White replaces Akwasi Asante.
Jack Higgins (York City) is shown the yellow card.
Jake Wright (York City) is shown the yellow card.
Substitution, York City. Daniel Nti replaces Justin Johnson.
Second Half begins York City 1, Solihull Moors 0.
First Half ends, York City 1, Solihull Moors 0.
Ryan Beswick (Solihull Moors) is shown the yellow card.
Andy Brown (Solihull Moors) is shown the yellow card.
Goal!  York City 1, Solihull Moors 0. Richard Brodie (York City).
First Half begins.
Lineups are announced and players are warming up.
Aidan Connolly scored an impressive brace as York bounced back from last week's defeat to Wrexham with an emphatic 4-0 victory over National League opponents Solihull at Bootham Crescent.