Manchester City also won 3-0 against Watford, while Newcastle United lost 2-0 to second-tier club Brighton.
London: Demba Ba made an immediate impact on his Chelsea debut in the FA Cup by scoring twice as the holders thrashed Southampton 5-1 on Saturday, while Newcastle was the only Premier League side to be ousted by lower-league opposition in the third round. A day after completing his move from Newcastle, Ba took just 35 minutes to score at Southampton to cancel out Jay Rodriguez's goal.
After further Chelsea goals from Victor Moses and Branislav Ivanovic, Ba netted his second before Frank Lampard wrapped up the rout from the penalty spot. The cup provided no respite for Newcastle from their Premier League struggles, with Alan Pardew's side losing 2-0 at second-tier club Brighton.
But Manchester City had no trouble ousting another League Championship club, Watford, with a 3-0 victory, while Tottenham beat third-tier club Coventry by the same score in a rematch of the 1987 final.
The biggest upsets were provided by fifth-tier nonleague sides overcoming second-tier opposition as Macclesfield beat League Championship leader Cardiff 2-1, and Luton defeated Wolverhampton Wanderers 1-0.
At Southampton, the 27-year-old Ba showed just how valuable he can be for Chelsea's quest for silverware this season as Fernando Torres was rested on the bench. The Senegal striker's 14th goal of the season - and first for Chelsea - came after Juan Mata initially attempted to score from an acute angle, cancelling out Rodriguez's opener.
Chelsea went in front on the stroke of half-time after Moses collected a cutback from Ashley Cole and struck into the net. Seven minutes into the second half, Ivanovic headed in Mata's cross, and Ba found the target again in the 61st after being setup by Eden Hazard.
The late penalty from Lampard - after Steven Davis handled - allowed the 34-year-old midfielder to move to joint second on Chelsea's all-time leading scorers list alongside Kerry Dixon.
As Southampton went out of the cup, it was a successful day for another south-coast side as Brighton eliminated Newcastle for the second successive season. Andrea Orlandi put Brighton ahead in the 33rd, hooking the ball into the net with the outside of his boot after meeting Wayne Bridge's cross.
Injury-depleted Newcastle's prospects took a further turn for the worse when captain Shola Ameobi received a second booking for his late tackle on David Lopez in 63rd. Brighton extended their lead in the 87th when Will Hoskins slotted the ball through goalkeeper Rob Elliot's legs after latching onto Lopez's through ball.
"We didn't have enough quality players on the pitch today ... the younger players have put as much effort in as they could," said Alan Pardew, whose Newcastle side is just above the Premier League relegation zone.
Three Premier League clubs face replays after being held by lower-league opposition. Wigan drew 1-1 with Bournemouth, Fulham was held by the same score by Blackpool, and Sunderland drew 2-2 with Bolton.
In a sign that the FA Cup's status may be declining in England, just 8,984 fans were at Loftus Road to see Queens Park Rangers take on Premier League rival West Bromwich Albion. Shane Long put West Brom ahead in the 79th, but Kieron Dyer earned QPR a replay by clinching a 1-1 draw in stoppage time.
Man City's preparations were disrupted in midweek by manager Roberto Mancini's training ground altercation with striker Mario Balotelli, who started from the bench against Watford. Instead, Carlos Tevez helped to steer City into the fourth round, netting from a free kick after 25 minutes before a header from Gareth Barry and a late strike from Marcos Lopes on his debut.
Aston Villa had to come from behind to defeat Ipswich of the League Championship. After Michael Chopra's first-half goal, Darren Bent equalised after the break after Andreas Weimann headed in Villa's winner.