Connolly converted Yassin Moutaouakil's cross from two yards in the 53rd minute and comfortably held on for their third straight home victory.
Tranmere's Sean McGinty came close to opening the scoring in a scrappy first half after 18 minutes, when Pompey goalkeeper Simon Eastwood had to tip his looping shot from the left over the bar.
Portsmouth striker Connolly should have put the hosts ahead after 38 minutes when Patrick Agyemang nodded Shaun Cooper's cross from the left into his path.
Connolly blazed his shot high over the bar and Agyemang fired wide of the upright in first-half stoppage time after giving Ash Taylor the slip and racing through on goal.
Connolly atoned for his sloppy finishing by giving Pompey the lead after 53 minutes when Moutaouakil fired across goal, giving him a two-yard tap-in he could not miss.
Pompey skipper Johnny Ertl nearly doubled his side's advantage three minutes from time when his fierce drive was beaten away by Tranmere goalkeeper Owain Fon Williams.
Tranmere were outclassed in the second period and home goalkeeper Simon Eastwood was rarely troubled as their promotion bid suffered a major setback.