Wales found the perfect response to Saturday's mauling by beating Cyprus in Cardiff to claim their first points of the Euro 2008 Group D qualifiers.
Koumas gave Wales a two-goal cushion just before half-time
Jason Koumas struck first with a header after 33 minutes and Robert Earnshaw converted Craig Bellamy's low cross to double the lead seven minutes later.
Captain Bellamy capped a magnificent individual display by adding a third with a cool finish on 72 minutes.
But Yiannis Okkas denied Wales a clean sheet with superb lob late on.
Wales manager John Toshack made just two changes to the side beaten comprehensively by Slovakia on Saturday - giving two youngsters their first starts in a competitive international.
Goalkeeper Paul Jones paid the price for his costly errors in the 5-1 defeat as Ipswich 22-year-old Lewis Price came in to win only his third cap.
And MK Dons centre back Craig Morgan, 21, made his full debut as he replaced Rob Edwards.
Cyprus were unchanged after their stunning 5-2 win over the Republic of Ireland on Saturday, but the first half gave no hint of the conflicting results the two sides brought into the match.
Wales had obviously done their homework on the Cypriot defence as they looked to expose their high defensive line with early balls over the top.
Bellamy beat the offside trap inside the first minute and looked to have been brought down by the onrushing Cyprus goalkeeper Michalis Morfis after beating him to the ball.
Wales quickly began to dominate possession, with Bellamy and Earnshaw linking well up front and Koumas pulling the strings in midfield.
The first clear opening fell to Earnshaw on 17 minutes, but the Norwich striker failed to keep his shot on target under pressure.
Koumas then grazed the post with a low drive before Morfis pushed Earnshaw's curling effort onto the post and out for a corner.
But Wales' luck soon changed as Morfis gifted Wales the lead by making a mess of trying to keep out Koumas' header.
Earnshaw missed a great chance to score a fourth in injury time
Koumas did well just to steer his effort on target from Simon Davies' far-post cross, but it proved too good for Morfis as he somehow allowed the ball to bounce over his body as he went down for a routine save.
Seven minutes later, Earnshaw finished off a fine move which was indicative of Wales' fine play to double the lead.
Bellamy again beat the Cyprus offside trap down the inside-right channel, and cut the ball inside perfectly for Earnshaw to finish confidently.
A dominant first half display ended with Koumas testing the Cyprus keeper with a curling effort from outside the box.
Wales almost threw away all their great work in the first half with some sloppy play in the opening seconds after the break.
Carl Robinson was dispossessed in a dangerous area, allowing striker Michalis Konstantinou to run inside the penalty area.
His shot was well saved by the outstretched foot of Price and then Efstathios Aloneftis put his effort wide as he followed up.
Earnshaw twice came close to putting the result beyond doubt around the hour mark.
His downward header from Bellamy's cross was saved well by Morfis and then he was denied by a contentious challenge in front of an open goal.
Cyprus looked a far greater threat in the second half, and began to pepper the Wales goal with long-range shots.
But any hope of a comeback were put to bed when Bellamy scored a goal of real quality.
The captain again found space through the inside-right channel to latch on to Davies' through ball and then chipped the advancing Morfis to score his first goal for Wales since February last year.
Bellamy then turned from hero to villain as he lost possession inside his own half which allowed Cyprus to cut the deficit.
Price, who had looked assured throughout, had no chance as Cyprus captain Okkas chipped him with an audacious lob from the right-hand side of the penalty area.
Earnshaw had a superb chance to add a fourth in injury-time, but his hesitancy after rounding the goalkeeper allowed Lambros Lambrou to clear his goalbound effort.
Wales: Price, Duffy (Edwards 78), Gabbidon, Nyatanga, Bale, Morgan, Robinson, Koumas (Ledley 76), Simon Davies, Bellamy (Parry 90), Earnshaw.
Subs Not Used: Brown, Crofts, Valentine, Cotterill.
Goals: Koumas 33, Earnshaw 39, Bellamy 72.
Cyprus: Morfis, Theodotou, Lambrou, Louka, Satsias (Yiasoumi 84), Michael (Charalambidis 45), Garpozis (Charalambous 45), Makrides, Aloneftis, Konstantinou, Okkas.
Subs Not Used: Georgallides, Elia, Alexandrou, Daskalakis.
Booked: Garpozis, Satsias.
Goals: Okkas 83.
Ref: Jacek Granat (Poland).