But Swansea showed the form which has taken them to second spot in the Championship in extending their unbeaten home run at the Liberty Stadium to 10 games.

Swansea gave an instant debut to Conor Hourihane, the Republic of Ireland midfielder signed on loan from Aston Villa this week.

But United States forward Jordan Morris had to wait for his introduction as his loan love from MLS side Seattle Sounders was not completed in time for him to feature.

Both sides made major changes from midweek league action – Swansea seven and Forest 10 – and the visitors found themselves behind inside seven minutes when Wayne Routledge scampered down the left.

Routledge, having possibly evaded an assistant's offside flag, delivered an excellent cross for Cullen to convert his second Swansea goal with a side-foot volley from eight yards.

The goal put Forest on the back foot and defender Carl Jenkinson was booked for clattering into Ryan Manning.

Swansea were in control without creating too many openings, but the pressure was suddenly applied to good effect before the half-hour mark.

Jordan Smith moved his feet quickly to stop Joe Worrall's header from dropping into his net for an unfortunate own goal.

But Forest failed to clear the resulting corner and Yan Dhanda set up Grimes from 25 yards, and the midfielder took advantage of no opponent pressing the ball to beat Smith inside his post with a vicious hit.

Swansea sensed the tie could be put to bed before the break and Manning produced a cross which Connor Roberts headed over.

Forest made a double substitution at the break with Cafu and Miguel Guerrero replacing Fouad Bachirou and Luke Freeman.

There was a strong response from Chris Hughton's side as Joe Lolley and Jenkinson had shots blocked, both times by the commanding figure of Ryan Bennett.

But Forest were back in the tie after 56 minutes when Lolley slalomed his way through the home defence before being upended by Marc Guehi.

Referee Kevin Friend could have pointed to the spot, but he let the play run an extra second and Knockaert swept home in style.

Swansea restored their two-goal advantage in controversial circumstances five minutes later.

Manning was running with the ball when appearing to move his foot towards Worrall and falling just inside the area.

But referee Friend pointed to the spot and Grimes stroked home his second with ease.

The tie was put beyond Forest after 67 minutes when Dhanda and Manning combined for Cullen to dispatch a low drive.

Cooper crowned victory by squeezing his shot under Smith's body to send Swansea into the next round.