Gor Mahia were level through Meddie Kagere before the interval but 19-year-old midfielder Kieran Dowell drilled in from the edge of the box in the 82nd minute to ensure Ronald Koeman's men enjoyed a winning start to pre-season.
Alongside Rooney, new signing Davy Klaassen also started for Everton with Aaron Lennon – the former England winger who is back in training with Koeman's first-team squad following a stress related illness.
Rooney saw a 17th-minute free-kick comfortably gathered by Boniface Oluoch but the Gor Mahia goalkeeper will have been a little disappointed when England's record goalscorer clinically caught him off his line in 11 minutes before the interval.
Gor Mahia were swiftly back on terms in the 38th minute, as Kagere powered in a header from a corner and the striker tested Maarten Stekelenburg in the Everton goal ahead of the half-time whistle.
Another new recruit, England defender Michael Keane, was introduced among a host of changes at the break along with Dowell – a member of England's triumphant Under-20 World Cup side - and Everton had long been in the ascendancy before he found the net.
Substitute goalkeeper Jerim Onyango excelled himself to deny Dominic Calvert-Lewin and Dowell either side of the winner, while Keane – stationed alongside Mo Besic at the heart of defence after Phil Jagielka and Ashley Williams combined for the first period – was able to help see out victory in relative comfort.