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.
Midfielder James Ward-Prowse was also recalled to the starting line-up in place of Steven Davis (knock).
Fernando Amorebieta replaced captain Brede Hangeland in the Fulham side after the Norway defender was ruled out due a nerve problem in his leg, while forward Bryan Ruiz (back) was passed fit.
Saints were almost gifted the lead after just four minutes as Philippe Senderos dithered on the ball and was robbed by Adam Lallana. He picked out Morgan Schneiderlin, whose shot was destined for the back of the net until Amorebieta intervened.
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.
It was only a matter of time before Saints increased their lead and two minutes before the break Lambert returned the favour to Rodriguez, guiding a header across goal for his strike partner to nod in.
Saints were not quite as fluent in the second half, but Rodriguez came close to a spectacular third goal when he volleyed wide after 68 minutes.
Steve Sidwell was off target with a shot eight minutes from time, yet Fulham never really threatened to make life difficult for their hosts.
Lallana ended a run with a shot that took a big deflection and landed on the roof of the net as Saints secured a comfortable win.
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