Fraser Forster Southampton Alexis Sanchez Arsenal
Arsenal forward Alexis Sanchez scores the winner against Southampton in their English Premier League gameReuters

Alexis Sanchez and Olivier Giroud were the difference makers for Arsenal  as the home team ran-out 1-0 winners over Southampton in their English Premier League game.

The Emirates crowd were wondering if it was going to be another difficult evening and result for Arsenal, before Sanchez struck right at the end to give the home supporters plenty to cheer about.

It was another unconvincing performance from the Gunners going forward, though, and even if they have found some good defensive stability – this game saw them keep their third straight clean sheet – they need to do better in the final third if they are to go on a big winning run and reduce the gap on the leaders in this busy festive period.

"We just kept going and we always believed in ourselves and it paid off completely," Arsenal vice-captain Per Mertesacker was quoted as saying by the club's official website. "They were one man down, we were a bit lucky because they had an injured player but we kept going and we deserved it in the end because we never gave up.

"We showed great spirit again. We needed that win desperately tonight because everyone won yesterday so we were a bit under pressure but I think we did well."

While Sanchez scored the winning goal, it was Giroud who made the difference in terms of attacking for Arsenal, with the striker's inclusion in the second half immediately bringing about a change.

Giroud has this extremely underrated ability of linking up play really well, and the France international showed just how much Arsenal have missed his services over the past three months with another really good performance.

While the victory has not brought about too much change in the Premier League table, considering most of the teams above Arsenal also won their respective games, the three points, their third straight in all competitions and second consecutive in the Premier League, will help breed confidence, which helps in going on a winning run, so necessary after their difficult start to the season.

"We've got to go on a winning run now," said midfielder Aaron Ramsey, whose pass it was which allowed Sanchez to sweep home from ten yards. "We've won our last three games now so hopefully we can continue that throughout the Christmas period."

"We want to continue this run and be more consistent than what we have shown this season -- that's our target," added Mertesacker. "In the Christmas period it's going to be busy but we're up for it."

Southampton will feel a little aggrieved with the loss, with their goalkeeper Fraser Forster, particularly, showing just why he is so highly rated with some wonderful saves.

However, the reality for Ronald Koeman's men is that they have now lost their last two games in the Premier League – against Manchester City and Arsenal – and they quickly need to find their winning groove, or that top four place could slip out of their grasp rather quickly.

"We had a good positive reaction after last Sunday, a good first half, good ball possession, a good chance off [Graziano] Pelle," Koeman told the Premier League's official website. "After an hour it was more difficult, Arsenal were pressing more but the difference was 11 vs 10.

"We were unlucky to get a player injured [Toby Alderweireld] after making all of our substitutions, you know they will create chances, and in the last few minutes they made it 1-0. Forster had a very good game."