Celtic manager Neil Lennon welcomes 'lift' brought by victory over St Mirren ahead of trip to Juventus The chronicle of defensive laxity, however, was extended when St Mirren conceded a corner kick and - after Forrest played it short and got a return ball from Gary Hooper - left Anthony Stokes unpoliced at the back post for what proved to be a headed winner. All the goals had been scored before the midway stage of the first half and the rest of the contest was deadlocked, with each goalkeeper producing a spectacular save. In Craig Samson's case it was to tip a venomous shot from Hooper on to the crossbar, while Forster dived to get a strong hand to a fiercely struck free-kick by Graham Carey, who had arrived as a late substitute. "This gives us a psychological lift going into Wednesday," Lennon said. It also keeps our season going. If we had lost today, that could have been our season over competitively. I want us to keep going. I don't want things to peter out. We gifted them a goal and they didn't have to work for it but we're going well - still in three competitions. Joe Ledley has come back and been exceptional for us. We've had a marvellous season and, hopefully, we can keep it going on Wednesday (against Juventus in the Champions League). To go there and win would be a tremendous way to end to the campaign. We want to make it look like the scoreline at Celtic Park was a little bit flattering to Juventus. In the afternoon's other Scottish Cup quarter-final tie, Falkirk beat Hamilton at New Douglas Park to reach the last four. The Bairns took the lead just before half-time when Tom Grant set up Blair Alston for a close-range drive and the same player repeated his scoring feat - this time from beyond the edge of the box - with 20 minutes left to play. Hamilton responded by sending on Andrew Ryan and he had an immediate effect when he struck from six yards to keep the issue in doubt. Strain as they might, however, the Accies could not score again and Steven Pressley's side edged through. The other two ties will be played today, the first being the lunchtime televised fixture from Dens Park where Dundee meet Dundee United. United won the two previous league derbies this season, but United have replaced Peter Houston with Jackie McNamara as manager, while John Brown has been installed as interim manager after Barry Smith's recent sacking. At Rugby Park two teams who have reached finals in the past year will meet in the other fixture. Hibs, beaten by Hearts in the 2012 Scottish Cup final, visit Kilmarnock, winners of last season's League Cup. Elsewhere, Motherwell brought themselves to within 16 points of Celtic in the SPL table with a win over Hearts - whose manager, John McGlynn, departed this week - at Tynecastle. Michael Higdon put Stuart McCall's side ahead after three minutes when he shot home from the edge of the box, and a deflection from Ryan McGowan sent an effort from Nicky Law across the line five minutes later. John Sutton raised Hearts" hopes with a headed goal just before the hour mark but Motherwell held on to increase their lead over Caley Thistle in third place and Ross County in fourth after the two Highland sides fought out a goalless draw in Dingwall.