In fact, that game was 35 years ago in November, it was Graham's home debut and coincidentally, it was in the fourth round of the League Cup at the Lane.
Not surprisingly, Graham's first notable action was a trademark crunching tackle. As all Spurs fans of a certain age will testify, that was his speciality!
'Robbo' recalls that night - November 4, 1980, a month after his Spurs debut - and his clashes against the Gunners with relish.
"I remember them all," he smiled this week, his eyes lighting up when talking about that November night.
"My room-mate for England was Kenny Sansom and my first game here was in the League Cup, I came off the bench and my first tackle was against Kenny and I put him right over the touchline.
"He said to me later ‘why did you go in that hard?’ and I just said ‘that’s how I play!’. He was great though, no problems. That's how it was then.
"On the pitch, there were no friends, especially between Spurs and Arsenal. People still talk about the tackle on Charlie Nicholas (1986) now! Afterwards, I just said ‘welcome to England’. It was a bit of fun really.
"We had some great battles but there was full respect as well. We still see some of those Arsenal lads now and play golf against them every year. We beat them at that as well!"
Below: Robbo (front, second from left) with Kenny Sansom (front, far right) on England duty with Glenn Hoddle - 1983
Plucked from non-league Weymouth by Keith Burkinshaw in May, 1980, Robbo was a key member of our great team of the early 1980s that won back-to-back FA Cups, reached the League Cup Final and then Robbo's golden moment, the UEFA Cup triumph of 1984.
His personal story is incredible as well, rising from non-league to Spurs, winning the FA Cup within a year and a first England cap three years later.
The versatile defender/midfielder went on to play 276 times for us between 1980-86 and was a huge fans' favourite - and recently voted into our Ultimate Team as centre-back.
And as we prepare to face Arsenal again in the Capital One Cup third round tonight, you can almost sense Robbo wanting to lace up his boots again!
"It's a special game, always will be," he added. "I remember beating them 5-0 here (April, 1983) and a great game at Highbury where we beat them 2-1 (New Year's Day, 1985) and Mark Falco scored.
"They were a good side in our time but I think we just got the better of them. We never feared them.
"The greatest night of all though was when we won the FA Cup semi-final at Highbury (against Wolves in 1981) and we were in the home dressing room, having just got to the FA Cup Final. That was a brilliant feeling."
Below: The Ultimate Spurs Team, as voted for by you!