The 19-year-old teamed up with Maclagan ahead of the grass season but lost her first match in Birmingham last week to eventual title winner Daniela Hantuchova.
Robson had a better draw here, facing Ukrainian qualifier Yuliya Beygelzimer, and she was much the stronger player in a 6-3 6-2 victory.
Robson has had an inconsistent season and she was erratic in the early stages, but a break for 4-2 in the opening set settled her down.
The teenager's serve is both a strength and a weakness but she had a good day with it today, powering down eight aces.
In the second round Robson will play former world number one Caroline Wozniacki, and she will hope to gain some revenge after losing to the Dane in the first round of the French Open.
Robson told the BBC: "There's still so many things I can improve on but I served really well today."
Wozniacki was watched today by boyfriend Rory McIlroy, who headed straight to Eastbourne from the US Open golf.
And the fifth seed managed only her second win in eight matches, albeit by retirement, with defending champion Tamira Paszek quitting with a leg injury trailing 6-2 2-2.
Paszek beat Wozniacki in the opening round at Wimbledon last year before going on to reach the quarter-finals but has had a miserable 2013, winning just two matches.
Elena Baltacha made it four British players through to the second round as she continued her fine form on grass with a 7-5 7-6 (7/3) victory over qualifier Kristyna Pliskova.
Former British number one Baltacha has dropped down the rankings after taking eight months out to have ankle surgery following the Olympics, but won her first trophy of the year last week in Nottingham.
The 29-year-old said: "I'm playing well. Last week gave me a lot of confidence to know I can put my body through five days of matches. It was an amazing week for me.
"This is my favourite tournament. Every year I love playing here."
However, there were first-round defeats for James Ward and Johanna Konta.
Ward took on world number 64 Bernard Tomic, who has been having a tough time on and off court recently.
Tomic was again watched by his father and coach John Tomic, who is awaiting trial in Madrid for allegedly assaulting his son's former hitting partner, a charge he denies.
Tomic Sr has been barred from obtaining accreditation for ATP events but not from buying tickets, although Wimbledon have said they will follow the French Open's lead and attempt to stop him entering the grounds.
The match was close but a break of serve late in each set proved Ward's undoing as Tomic prevailed 6-3 6-4.
British number three Konta is at a career-high ranking of 137 and has been playing well on the grass.
She had extra reason to want to do well given Eastbourne has been home since her family moved to Britain from Australia eight years ago, but she found world number 44 Hsieh Su-wei too tough, losing 6-4 6-3.
There were straightforward wins for second seed Li Na, third seed Angelique Kerber, former Wimbledon champion Petra Kvitova and Sam Stosur.
The only hold-up for Li in her 6-2 6-4 win over Alize Cornet came when a spectator fell ill and received lengthy treatment in the stands at Devonshire Park.
There was a major upset late in the day as top seed and last year's Wimbledon finalist Agnieszka Radwanska was dumped out in the first round by Jamie Hampton.
Hampton, 23, is one of a large crop of promising young Americans and she has been having a good season, reaching the fourth round of the French Open.
Radwanska fought back from a break down early on to take the first set to a tie-break but it was Hampton who won it, and the underdog dominated the second set to win 7-6 (7/2) 6-2.