Midfielder Lampard netted his 20th League Cup goal while Salomon Kalou and Florent Malouda were also on the scoresheet as Chelsea swept aside FA Cup holders Portsmouth.
Scolari, targeting an unprecedented quadruple, named a strong line-up, with striker Didier Drogba making his first start since last season's Champions League final after recovering from a knee injury.
Injury-hit Portsmouth were without Sol Campbell, Jermain Defoe and former Chelsea midfielder Lassana Diarra.
Chelsea dominated possession but had to wait until nine minutes before the interval to turn their superiority into a goal when they were gifted the lead.
Michael Ballack was hacked down by a reckless late tackle from Portsmouth's Algerian defender Nadir Belhadj, leaving referee Steve Bennett with no option but to award a penalty.
Lampard stepped up to send England team-mate David James the wrong way and pick out the bottom left-hand corner of the net as he registered his fourth goal of the season.
Malouda doubled four-time winners Chelsea's lead on the stroke of half-time to make it eight goals conceded by Portsmouth in just one-and-half matches following their 6-0 drubbing by Manchester City on Sunday.
Kalou picked out Malouda midway inside Pompey's 18-yard box and the much-maligned Frenchman slotted the ball past James with a well-struck shot on his weaker right foot.
Lampard, who scored in Chelsea's 4-0 Premier League win over Portsmouth on the opening day of the season, wrapped up the Londoners victory four minutes into the second half, thanks to a huge error from veteran James.
Kalou came bursting down the right touchline before putting in a tame cross, which James punched straight onto Lampard's thigh and the ball bobbled into an empty net.
Ivorian Kalou put the seal on a man-of-the-match performance by notching Chelsea's fourth in the 64th minute.
He was given far too much freedom down the right before cutting in on his left foot and rifling past James at his near post.