Jon Walters' early header means Stoke hold a 1-0 advantage against Hajduk Split after the first leg of their Europa League third qualifying round tie at the Britannia Stadium.
The Potters, playing in major European competition for the first time in 37 years, took the lead in the third minute when Walters was allowed the space to nod in Matthew Etherington's measured cross.
Despite dominating for much of the match thereafter, though, they were unable to find the second goal which would make next week's trip to Croatia for the return leg more comfortable.
Fulham endured a frustrating evening in Croatia as RNK Split eked out a goalless draw.
The Cottagers failed to impress at Dugopolje's Stadion Hrvatski Vitezovi and struggled to unleash a menacing attack at any stage of the first leg.
Split proved the more dangerous force and had two gilt-edged chances to score, with Ante Erceg fluffing a one-on-one opportunity in the sixth minute before substitute Duje Cop missed an equally inviting chance in the dying minutes of the game.
Hearts started well at Videoton's Sostoi Stadium but fell behind in the 32nd minute.
Hearts were down to 10 men at the time with Ian Black off the pitch receiving treatment for a knock when Istvan Sipeki lobbed Kello.
Laszlo Bartha's initial effort from outside the box was blocked by Eggert Jonsson and Sipeki struck the bouncing ball over the stranded goalkeeper.
However, Hamill levelled on the stroke of half-time following a foul on John Sutton in the penalty area.
St Patrick's face an uphill battle to reach the play-off round of the Europa League after losing the first leg of their third qualifying round tie 2-0 against Karpaty Lviv in Ukraine.
Artem Fedetskiy opened the scoring after 34 minutes and the hosts continued to dominate proceedings, with St Patrick's struggling to test Karpaty goalkeeper Martin Bogatinov.
The League of Ireland side looked like they would take Karpaty back to Richmond Park with only a one-goal deficit, but Belarus international Andrei Voronkov came off the bench to double the hosts' lead in stoppage time.
Sligo Rovers boosted their hopes of progressing through to the next stage of the Europa League after holding Vorskla Poltava to a goalless draw in Ukraine.
Hosts Vorskla created the majority of the chances in the match but they could find no way past Brendan Clarke in the visiting goal.
The second leg will take place at The Showgrounds next Thursday, when Paul Cook's men will hope to book their place in the play-off round.