The match was played at the TNA Stadium in Tarkwa, with Kelvin Nkrumah scoring the decisive goal in first-half stoppage time.
After a cagey opening period, the 19-year-old midfielder broke the deadlock in the second minute of added time at the end of the first half, giving Medeama a 1–0 lead at the interval.
Port City pushed for an equaliser after the restart but struggled to create a clear opening against a disciplined Medeama defence.
The visitors' task became even more difficult when Ransford Lartey was sent off in the 66th minute, leaving Port City with 10 players for the remainder of the match.
Medeama took advantage of their numerical superiority to control the closing stages and held on for another clean sheet and three points.
The victory takes Medeama to eight points, level with FC Samartex but ahead on goal difference at the top of the table. Port City suffered their first defeat of the campaign and dropped to fifth.
The result also completes Medeama's outstanding early-season schedule after their Matchday 2 fixture was postponed because of their CAF Champions League involvement.
Nkrumah is enjoying a productive spell, having also scored in Medeama's 4–1 victory over Basake Holy Stars on 27 September. His latest goal gives him two goals in his last two matches.
Medeama will now turn their attention to their next league fixture away to Debibi United on 4 October.
• Medeama SC: 1
• Port City FC: 0
• Goal: Kelvin Nkrumah 45+2'
• Red card: Ransford Lartey 66' (Port City)
• Venue: TNA Stadium, Tarkwa
• Competition: Ghana Premier League, 2026/27 season