The result stretched the Steelers' unbeaten run to five matches and came 24 hours after they edged out fellow title hopefuls Belfast Giants in a nine-goal thriller at the Motorpoint Arena.
Player-coach Ben Simon scored the only goal of the first period in Dundee before his side took the game away from the hosts with goals from Rod Sarich, Jonathan Phillips, Neil Clark and Jeff Legue in the second.
Any hope the home side ehad of a comeback were extinguished early in the third by Ashley Tait's 18th goal of the season in the 44th minute before Rob Dowd wrapped up the scoring just under a minute later.
The result leaves the Steelers two points behind Cardiff, who picked up four points themselves over the weekend when they followed up a 4-0 home win over the Braehead Clan on Saturday with a hard-fought
3-1 win at Hull Stingrays last night.
Penalty trouble in the third period almost cost the Steelers dearly in front of their home fans on Saturday night, but they held on for a 5-4 win over Belfast.
Brandon Benedict gave the visitors an early lead but goals from Derek Campbell and Rob Globke put the home side ahead just after the halfway mark.
The crucial spell came just before the second interval, however, when Legue's strike at 39.01 was followed by a bullet from defenceman Steve Munn just six seconds later.
Belfast reduced the deficit early in the third through Craig Peacock before Sarich restored the home side's three-goal advantage. Goals from Peacock and then Colin Hemingway made it a one-goal game with a minute to go but the Steelers hung on.
Hull went into last night's match with Cardiff on the back of a 3-1 defeat at Nottingham Panthers on Saturday.
Jereme Tendler had given player-coach Sylvain Cloutier's side a first-period lead but goals from Marc Levers Jade Galbraith and Rob Bellamy kept the home side's fading title hopes alive.
Cardiff opened the scoring in Hull last night through a fourth-minute powerplay strike from the prolific Jon Pelle. Stuart Macrae doubled the advantage at 20.15 and although Trevor Read halved the deficit midway through the second, a 43rd-minute strike by Mark Richardson ensured the Stingrays ended the weekend empty-handed.