England striker Rickie Lambert was a substitute in the draw at Manchester United last weekend, but marked his return to the starting line-up by scoring his third Saints goal this season following an assist from Rodriguez.
Saints dominated the first half and were rewarded with a second goal just before the break, when Lambert this time presented Rodriguez with a simple opportunity to head home from close range.
Mauricio Pochettino's side have made their best start in the top-flight for 30 years and can boast the best defensive record in the league, having conceded just three times in their first nine games.
They were worthy winners as Martin Jol’s Fulham paid the price for a poor display and dropped down to 14th in the table.
Lambert replaced big-money signing Dani Osvaldo, who was not even on the bench amid reports he is unsettled at St Mary's.
The home side moved in front after 20 minutes when Ward-Prowse's corner was flicked on by Rodriguez and an unmarked Lambert nodded home at the far post.
Rodriguez almost doubled his side’s advantage a minute later as he breached the Fulham defence far too easily and only a fine fingertip save from Maarten Stekelenburg prevented a fine individual goal.
The Cottagers were struggling to contain the home side and Lambert rattled the post with a venomous drive from just outside the penalty area before Stekelenburg kept out another Lambert header.
