Rodriguez was the difference between Mauricio Pochettino's team and their Spanish third-tier opponents, as he struck either side of a David Cano goal to give the St Mary's outfit a winning start to their preparations ahead of the new Premier League season.
Pochettino named a strong squad for the game in Palafrugell, Catalunya, with new signings Victor Wanyama and Dejan Lovren included alongside regular first-teamers such as Adam Lallana and Luke Shaw on the bench.
But it was former Burnley striker Rodriguez who stole the show, as his attacking prowess caused no end of problems for the hosts.
The 23-year-old had the ball in the net as early as the 12th minute, but was denied by the offside flag. However, he continued to wreak havoc and was rewarded 16 minutes later when he capitalised on a mix-up between Llagostera keeper Jose Moragon and defender Pere Segarra to slot home the opener.
Pochettino made 10 changes at the break, with only star man Rodriguez remaining on the pitch from the first half at the start of the second period. Rickie Lambert, Wanyama, Lovren and Shaw were among those brought on.
Rodriguez almost doubled the visitors' advantage on the hour-mark when he ran on to a through ball from strike partner Lambert, only to be denied at point-blank range by Llagostera's substitute goalkeeper Nico Ratti.
And the home side took full advantage of this reprieve to draw level just two minutes later when defender David Cano nodded Adriano Garcia's corner beyond Paulo Gazzaniga.
However, Rodriguez was in no mood to be upstaged and he restored the Premier League outfit's lead on 67 minutes. Ratti saved well from Lallana's shot, but the striker was on hand to convert the rebound.
That proved to be the Englishman's last contribution as he was taken off for young midfielder James Ward-Prowse.
Ex-Celtic man Wanyama then went close to his first goal in Southampton colours as he let fly with a vicious half-volley that went just wide two minutes from time as the Premier League team's superior fitness and quality shone through in the closing stages.
However, they could not add to their lead and had to settle for a 2-1 victory. Next up for Pochettino's men is a friendly at Palamos on Saturday.
