Rooney marked his 100th cap with a 44th international goal from the penalty spot in the 59th minute, restoring parity after Jordan Henderson's own goal put the visitors ahead against the run of play two minutes earlier.
Welbeck then took centre stage with a quickfire double to star as England's match-winner, as he did in the opening 2-0 Group E triumph in Switzerland
Both teams struggled to get to grips with a Wembley pitch showing the full effects of last weekend's NFL action during a forgettable first half.
But Roy Hodgson's team banished their earlier uncertainty, belatedly finding the creativity and verve required to maintain their 100 per cent record and establish a comfortable advantage at the top of the pool.
Nathaniel Clyne was handed an England debut but there was an early scare when the Southampton right-back allowed Andraz Kirm to steal in behind him, though he could only wastefully loop a tame header into Joe Hart's gloves.
Clyne soon settled into the contest, skipping impressively down the right flank and cutting back for Rooney to set up Raheem Sterling, although the Liverpool forward dragged his 17th-minute shot wide.
Centurion Rooney had his first sight of goal four minutes later, only to blaze a half-volley over when Welbeck chested into his path 25 yards out - the Arsenal man unable to find power or direction on the end of Sterling's deflected cross soon after.
Slovenia captain Bostjan Cesar was fortunate to escape punishment when he appeared to elbow Adam Lallana in the 36th minute before Welbeck fired wide from the edge of the area with Rooney well-placed.
Neither team managed an attempt on target during the first period and, though England played with greater purpose following the resumption, they fell behind in sloppy fashion.
Lallana needlessly bundled Kirm to ground and Henderson headed the midfielder's dangerous delivery into his own goal under pressure.
The hosts' response to their first goal conceded in the qualifying campaign was instant, with Rooney drawing a foul from Cesar in the area and blasting home from the spot despite penalty specialist Samir Handanovic getting a firm touch on the ball.
Hodgson's men pressed relentlessly to build on Rooney's equaliser and they were rewarded in the 66th minute when a combination of Handanovic and Miso Brecko could not fully clear Lallana's low, angled effort - Welbeck on hand to send a volley into the ground and spinning into the net.
England's earlier lethargy was a thing of the past by the time Welbeck slickly exchanged passes with Sterling to coolly slot home his second 18 minutes from time and wrap up the points.
Hodgson's side can now turn their attentions to Tuesday's friendly clash with Scotland, enjoying the safety and comfort of top spot in their group.
